“The fact that Republicans are willing to even consider the embarrassment of nominating Collins — who has been indicted — for another local G.O.P. position, makes clear just how nervous national Republicans are about losing the House,” said Meredith Kelly, a spokeswoman for the Democratic Congressional Campaign Committee.

Further complicating matters are New York’s byzantine election laws: Mr. Collins is slated to be on the ballot not just on the Republican line but also as an Independence Party candidate. That party, too, would have to agree and find a way to remove him.

Mr. Collins is also the nominee of the Conservative Party. Michael R. Long, the party chairman, said on Saturday that he had spoken with Mr. Collins and would do whatever was necessary to remove him from the ballot. “If he so desires, that’s fine with me,” Mr. Long said.

The Democratic candidate in the race, Nate McMurray, the town supervisor of Grand Island, had only $80,000 in his campaign account when the indictment was announced — far less than is typically needed to wage an aggressive challenge.

Mr. McMurray had not been the preferred candidate of Democratic leaders in New York, led by Gov. Andrew M. Cuomo, who had recruited Lt. Gov. Kathy Hochul for the seat. She declined and instead ran for re-election.

Mr. McMurray called on Mr. Collins to resign immediately, saying he “should not be running for this or any other seat, a fact that the local Republican Party knew full well when they endorsed and celebrated him while he was under investigation for securities fraud.”

Mr. Collins’s decision to suspend his re-election bid set off an immediate scramble for the Republican nomination, with Stefan Mychajliw, the Erie County comptroller, announcing his candidacy within hours. In a preview of what will most likely be a polarized and partisan race over the next three months, Mr. Mychajliw called Mr. McMurray “radical” three times in a four-paragraph statement.