Indeed, the whole process is akin to a game of musical chairs, and there is some fear that with Mr. Collins possibly moving down the ballot, and one or more Republicans moving up, the end result could leave some elected official without a seat, or in an unfavorable election.

Last month, the heads of the eight Republican county committees interviewed nine potential replacement candidates. They included state senators and Assembly members, county legislators, the Erie County comptroller and even Carl Paladino, an ally of Mr. Trump who unsuccessfully ran for governor in 2010, and whose racist remarks in 2016 about Michelle Obama made headlines.

One possible sequence would see Mr. Collins replaced with a state senator, whose empty ballot line would then be filled by a current Assembly member. A county lawmaker would then move into the Assembly line.

But if Democrats were to successfully challenge the nomination of Mr. Collins for a town clerkship, he would be placed back on the congressional ballot — leaving whoever received the Republican nod to replace him out in the cold.

The uncertainty may have played a factor in why a leading candidate to replace Mr. Collins recently withdrew his name from consideration. State Senator Michael H. Ranzenhofer, who was interviewed on Aug. 21 along with the other candidates, said in a statement: “The chairmen and chairwomen who will make this very important decision have been thrust into uncharted waters and a very difficult decision.”

One interested contender, Stefan I. Mychajliw, the county comptroller, even used the uncertainty as part of his pitch to party leaders, noting that he is not up for re-election this year. “I’m the strongest bet and the safest bet,” he said in a phone interview. “If I’m selected and Congressman Collins stays on the ballot, there’s nothing lost. There is no negative consequence down the ballot.”

Since the indictment against Mr. Collins, the campaign of Mr. McMurray, 43, has received a burst of energy, with national Democrats suddenly paying attention to a race that had been considered a sure bet for Republicans. Registered Democrats in the district are outnumbered by Republicans, 191,000 to 149,000.