The chairman, who spent two decades in the state Legislature, billed himself as the strongest Republican candidate and said he didn’t think his entry into the race made it more difficult for his party to win. "You've got to have Republicans in the race who are capable of winning the race," he said. "Obviously, I think that's me."

Amodei said he spoke with Lt. Gov. Brian Krolicki (R) — who opted against running in the special election — before deciding to get into the race. "If this had been a regular cycle, we'd probably both be in the primary," he said.

During the special election campaign, Amodei said he plans to reach out to Democrats and Independents in addition to appealing to Republicans. "I do think you have to talk to them," he said. 

Angle is one candidate who may have trouble cultivating her appeal beyond the GOP base, but Amodei wouldn't dismiss her chances. "You can't ever count Sharron out," he said. "I'm certainly not going to do that."

Meanwhile, if the party's attempt to change the open format fails, the state Republicans may choose to back a candidate, according to a Nevada Republican source. Even if he or she isn't the designated nominee on the ballot, it would help tilt the scales. Amodei would be the runaway favorite for that type of endorsement, but said he had "no knowledge" of the party's plans.

On the Democratic side, the state party is staying neutral, officials say, despite facing a similar challenge because of a bevy of candidates running for the seat. 

Former congressional candidates Jill Derby and Nancy Price have remained in the race despite the entry of state Treasurer Kate Marshall into the field on May 4. But the Democratic field could change ahead of the May 25 filing deadline.

Heller was sworn in as the junior senator from Nevada on Monday, replacing former Sen. John Ensign (R-Nev.).

--This post was originally published at 1:37 p.m.