
634 F.3d 895 (2011)
Pablo DELAPAZ and Michael Sarkauskas, Plaintiffs-Appellants,
v.
Robert RICHARDSON, Defendant-Appellee.
No. 10-1215.
United States Court of Appeals, Seventh Circuit.
Argued December 8, 2010.
Decided February 14, 2011.
*897 Mitchell A. Kline (argued), Attorney, Chicago, IL, for Plaintiffs-Appellants.
J. Mark Powell (argued), Attorney, City of Chicago Law Department, Chicago, IL, for Defendant-Appellee.
Before FLAUM and EVANS, Circuit Judges, and McCUSKEY, District Judge.[*]
FLAUM, Circuit Judge.
Appellants Pablo Delapaz and Michael Sarkauskas work for the City of Chicago's Department of Streets and Sanitation ("DSS"). Under DSS Commissioner Al Sanchez, Delapaz and Sarkauskas were temporarily assigned to "act up"meaning to work above their titled position for additional pay. Shortly after Michael Picardi replaced Sanchez as DSS Commissioner, appellee Robert Richardson (the Deputy Commissioner of the Bureau of Street Operations) informed Delapaz that he was being returned to his titled position. Richardson told Delapaz to inform Sarkauskas that he too would be returned to his titled position. Appellants contend that Richardson demoted them because of their political affiliation with the Hispanic Democratic Organization ("HDO"), while Richardson maintains that he simply was carrying out Picardi's directive that all acting employees be returned to their permanent positions.
Delapaz and Sarkauskas brought this suit against Richardson (and others, who we need not consider in this appeal) under 42 U.S.C. § 1983. The suit charges that Richardson violated their First Amendment right to free association by demoting them on the basis of their political affiliation. The district court granted summary judgment in favor of Richardson; Delapaz and Sarkauskas appealed.
For the reasons set forth below, we affirm.

I. Background
Appellants both are long-time City employees. Delapaz has been employed by the City since 1984, and has held the position of foreman of motor truck drivers in the DSS since 1998. Sarkauskas began working for DSS as a motor truck driver ("MTD") in 1979. Both Delapaz and Sarkauskas have volunteered for the HDO. Delapaz has done so since 1996 or 1997, Sarkauskas, since 2001.
At times, the City assigns current employees to fill open positions above their official titled positions for a limited time. For example, an MTD might be assigned *898 to be an acting foreman of MTDs. That practice is known as "acting up." In 2001, then-DSS Commissioner Sanchez assigned Sarkauskas to be an acting foreman in the Bureau of Sanitation, one of seven bureaus within the DSS. In 2002, Sanchez made Delapaz acting General Foreman of the Bureau of Street Operations, another DSS bureau. Later, Sanchez transferred Sarkauskas to the Bureau of Street Operations, where he worked directly under Delapaz as an acting foreman.
In June 2005, Picardi became DSS Commissioner, and Richardson was named Deputy Commissioner of the Bureau of Street Operations. Picardi testified that, as DSS Commissioner, he had the authority to assign employees to "act up" in title and to return employees from acting positions to their titled positions. According to Picardi, shortly after he became Commissioner, he ordered all acting employees returned to their permanent positions because of "budgetary and operational necessity." Richardson testified that in June 2005 Picardi directed him to inform all Bureau of Street Operations employees who were acting up that they would be returned to their titled positions. Picardi testified that he made an exception to that sweeping order for purposes of snow removal, authorizing Richardson to assign MTDs and MTD foremen to "act up" as necessary to clear snow. Picardi further testified that he delegated his authority regarding "acting up" decisions to the Deputy Commissioners, including Richardson.
In the summer of 2005, Richardson told Delapaz he would no longer be acting up, and would return to his position as MTD foreman. According to Delapaz, during that conversation Richardson said, "You know, Pablo, you are no longer the General Foreman. As a matter of fact, you are in charge of nothing, and your guy is gone." Delapaz testified that he did not know whether Richardson was aware that he volunteered for the HDO, and that Richardson did not indicate who he meant by "your guy." Two weeks later, at Richardson's direction, Delapaz informed Sarkauskas that he would no longer be an acting foreman. Sarkauskas testified that all ten of the acting MTD foremen in the Bureau of Street Operations were returned to their titled positions as MTDs at that time. Sarkauskas further testified that not all of those individuals were affiliated with the HDO.
The following fall, Richardson assigned Rodney Sernek to act as a general foreman during the hours needed for snow removal only. Sernek had made contributions to and done campaign work for Alderman Richard Mell, despite the fact that he did not live in the Alderman's ward. Delapaz contends that Sernek "replaced" him as quid pro quo for Sernek's support of Mell. Sarkauskas testified that after he was returned to his titled position, Daniel Gasdziak was made an acting foreman, and that Gasdziak held that position for a year and a half. According to Richardson, he did not assign Gasdziak to act up until April 30, 2006.
Richardson testified that he neither knew that Sernek was affiliated with Alderman Mell, nor whether Delapaz or Sarkauskas was affiliated with any political organization. Richardson also testified that he is not affiliated with and has not made political contributions to Alderman Mell.
Delapaz and Sarkauskas claim that their First Amendment rights were violated when they were returned to their titled positions ("demoted" in their words) because they belonged to the HDO and did not support Alderman Mell. The district court granted summary judgment in favor *899 of Richardson, and Delapaz and Sarkauskas appeal.

II. Discussion
We review the district court's grant of summary judgment de novo, construing all facts and reasonable inferences in the light most favorable to Delapaz and Sarkauskas. Forrest v. Prine, 620 F.3d 739, 742-43 (7th Cir.2010). A grant of summary judgment is appropriate when no genuine issues of material fact exist, and the moving party is entitled to judgment as a matter of law. FED.R.CIV.P. 56(c); Anderson v. Liberty Lobby Inc., 477 U.S. 242, 255, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986).
An individual's affiliation with a political party enjoys First Amendment protection. See Gunville v. Walker, 583 F.3d 979, 984 (7th Cir.2009). The firing or demotion of an employee based on party affiliation violates the First Amendment. Id. While an exception exists for jobs that cannot be performed effectively without party loyalty, the parties agree that political affiliation is not an appropriate consideration for appellants' DSS positions. Id.
Before reaching the merits of appellants' First Amendment claim, we consider the viability of their § 1983 claim more generally. To survive summary judgment, a plaintiff claiming a violation of § 1983 must produce evidence that the defendant "caused or participated in [the] constitutional deprivation." Vance v. Peters, 97 F.3d 987, 991 (7th Cir.1996). See also Caldwell v. City of Elwood, 959 F.2d 670, 672 (7th Cir.1992) (section 1983 plaintiff must "`connect the violation to the named defendants'") (quoting Brownlee v. Conine, 957 F.2d 353, 354 (7th Cir.1992)). Here, appellants admitted in their Local Rule 56.1 response, that "Picardi ordered that all employees who were currently acting up in a higher rated position . . . be returned to their titled positions, except to the extent necessary for specific operational needs." Presumably in reliance on that admission, the district court believed it to be "undisputed that the decision to demote Delapaz and Sarkauskas was made by Picardi, not by Richardson." Appellants now argue that the district court got it wrong. Ignoring their own admission, appellants point to another paragraph in their 56.1 response, in which they denied that Picardi told Richardson to inform Delapaz and Sarkauskas about their demotions. Appellants based that denial on Picardi's statement that he delegated the authority to assign employees to "act up" in title and to return employees to their career service titles to the Deputy Commissioners of the seven DSS bureaus.
Rule 56.1(b)(3) of the Local Rules for the Northern District of Illinois requires parties opposing a summary judgment motion to file a concise response to each numbered paragraph in the moving party's Local Rule 56.1 statement. The obligation set forth in Local Rule 56.1 "is not a mere formality." Waldridge v. American Hoechst Corp., 24 F.3d 918, 924 (7th Cir.1994). Rather, "[i]t follows from the obligation imposed by Fed.R.Civ.P. 56(e) on the party opposing summary judgment to identify specific facts that establish a genuine issue for trial." Id. The Rule is designed, in part, to aid the district court, "which does not have the advantage of the parties' familiarity with the record and often cannot afford to spend the time combing the record to locate the relevant information," in determining whether a trial is necessary. Id. at 923-24.
Here, the district court relied on appellants' admission, as it was entitled to do. We, too, are entitled to rely on that admission, and are inclined to hold appellants to their 56.1 response. In light of their admission that Picardi made the demotion *900 decision, appellants cannot establish § 1983 liability against Richardson.
Even if we were to disregard the admission, appellants' § 1983 claim fails because they waived the issue of Richardson's personal involvement in the demotion decision. In his summary judgment brief, Richardson argued that appellants had failed to demonstrate that he participated in the decision to demote them. As the district court noted, appellants did not address that argument in their response brief below. Consequently, they waived the issue. See Hicks v. Midwest Transit, Inc., 500 F.3d 647, 652 (7th Cir.2007) (arguments not raised before the district court are waived on appeal).
Moreover, appellants' § 1983 claim cannot survive summary judgment for the additional reason that they have not demonstrated the existence of a genuine issue for trial as to Richardson's involvement. Appellants rely on Picardi's statement that he delegated the authority to make acting up decisions to the Deputy Commissioners, including Richardson. However, that statement is not in conflict with Picardi and Richardson's testimony that, immediately upon assuming responsibility as DSS commissioner, Picardi decided to return all employees who were acting up to their titled positions. Picardi may have initially ordered all acting employees returned to their titled positions, and thereafter permitted Deputy Commissioners to assign employees to "act up."
Apart from their inability to establish § 1983 liability against Richardson, appellants failed to make out a prima facie claim for violation of their First Amendment rights. To establish a prima facie First Amendment claim, public employees must present evidence that (1) their speech was constitutionally protected; (2) they suffered a deprivation likely to deter free speech; and (3) their speech was the but-for cause of the employer's actions. See Gunville, 583 F.3d at 983; Fairley v. Andrews, 578 F.3d 518, 525-26 (7th Cir. 2009) (requiring but-for causation). Only the third elementcausationis at issue here. We have held that, to demonstrate causation in this context, plaintiffs must show that the defendant knew of their party affiliation. Gunville, 583 F.3d at 984.
In an effort to demonstrate that Richardson knew Delapaz was affiliated with the HDO, appellants point to the "your guy" comment. Construing all facts and reasonable inferences in the light most favorable to appellants, it can reasonably be inferred that Richardson was referring to Sanchez. However, appellants' brief on appeal never addresses Sanchez's relationship to the HDO, or Richardson's knowledge of any such relationship. Nor did appellants link Sanchez to the HDO in the brief in opposition to summary judgment or the 56.1 statement they filed in the lower court. Summary judgment is the "put up or shut up" moment in litigation. Goodman v. National Sec. Agency, Inc., 621 F.3d 651, 654 (7th Cir.2010). As such, appellants were required to present evidence on which a reasonable jury could rely tending to prove their claim. Id. Because appellants present no evidence linking SanchezDelapaz's "guy"to the HDO, no jury could conclude that Richardson demoted Delapaz because of his political affiliation with the organization.
Appellants present no evidence that Richardson knew Sarkauskas was affiliated with the HDO. Instead, Sarkauskas contends that the timing of his demotiontwo weeks after Delapaz'sis suspicious. However, it is unclear how that timing is at all suspicious, particularly because nine other MTDssome of whom Sarkauskas admits were not affiliated *901 with the HDOalso were returned to their titled positions at that time. In short, Sarkauskas presents nothing more than his own unsubstantiated speculation as to the reason for his demotion; such conjecture alone cannot defeat a summary judgment motion. Rockwell Automation, Inc. v. National Union Fire Ins. Co. of Pittsburgh, 544 F.3d 752, 757 (7th Cir.2008).

III. Conclusion
For the foregoing reasons, we AFFIRM the district court's grant of summary judgment in favor of Richardson.
NOTES
[*]  The Honorable Michael P. McCuskey, United States District Court for the Central District of Illinois, sitting by designation.
