Donald J. Trump's Republican rivals are seeking to make a stand against him in the Nevada caucuses on Tuesday, their last chance to slow his momentum before a dozen states vote on the party's presidential nomination next week.
But it may be difficult to stop Mr. Trump in Nevada, where he has enjoyed a high profile because of his business dealings in Las Vegas and where only a small number of voters have typically participated in the caucuses.
Senators Ted Cruz of Texas and Marco Rubio of Florida have established serious operations in the state, and both campaigned there in advance of Tuesday's contest. They may once again be battling for second place rather than for a real shot at dethroning Mr. Trump.
That battle took on a sharply personal tone on Monday, when Mr. Cruz fired a top aide because he had spread a video that misrepresented comments Mr. Rubio made about the Bible. Mr. Cruz said he was upholding his campaign's standards of integrity. Mr. Rubio's team fired back that Mr. Cruz, not his aide, was the one with the character problem.
Robert F. List, a former governor of Nevada who is aiding Mr. Rubio's campaign, called Mr. Trump the favorite to win in the state. But he said Mr. Rubio could consolidate late support there based on the perception that he is the candidate best equipped to win a general election.
"Trump is still the guy to beat in Nevada, but I see this being a good test between Rubio and Cruz," Mr. List said, adding, "I think Nevada Republicans are hungry for a winner this year."
Nevada may have a limited impact on the race for presidential delegates with only 30 at stake, slightly more than 1 percent of the total, and they will be handed out proportionally, based on the caucus vote. Barring an enormous landslide, Mr. Trump may pad his lead in the delegate count by only a modest handful.
Mr. Trump has approached the Nevada race with boastful confidence, describing it as a step toward a sweeping victory in the 12 states that vote next week on Super Tuesday. In his Saturday night speech in South Carolina, Mr. Trump told supporters he wanted a "big win in Nevada" that would help him lock down the nomination in short order.
But the state is a test both of Mr. Trump's staying power and of his rivals' abilities to remain competitive in a longer race.
It may help resolve whether Mr. Rubio's appeal to mainstream Republicans or Mr. Cruz's strength among evangelicals and conservative activists is the more plausible path to defeating Mr. Trump.
Mr. Rubio has quickly gathered local Republican leaders behind him in Nevada, after Jeb Bush, the former Florida governor, withdrew from the race on Saturday night. Senator Dean Heller, a former Bush backer, endorsed Mr. Rubio over the weekend, and Representatives Mark Amodei and Cresent Hardy followed suit.
Mr. Cruz is seen as having powerful appeal in rural areas of Nevada, where activist conservatives have often fared well in primary elections and where hostility to the federal government runs high.
For Mr. Cruz, a strong showing in Nevada could ease concerns about the durability of his campaign that have surfaced since his victory in the Iowa caucuses on Feb. 1. He has struggled to maintain his position in the race and came in slightly behind Mr. Rubio in South Carolina, a state Mr. Cruz once seemed well positioned to win.
A victory by Mr. Trump would leave him as the winner in three of the four early-voting states, with Iowa, where he narrowly lost to Mr. Cruz, his lone defeat.
The most valuable endorsement in the state would most likely come from Gov. Brian Sandoval, a popular Republican, but he is not expected to pick a side.
Pete Ernaut, a Republican political consultant who advises Mr. Sandoval, said he believed the caucuses were a "jump ball" between the three leading candidates. In a low-turnout event like the caucuses, he said, the strength of their campaign organizations could be decisive.
"If I had to guess, I would say Trump has a bit of an advantage," said Mr. Ernaut, a former Bush supporter. "But in a caucus, rather than a primary, anything can happen."
There is little history to guide analysis of the Nevada caucuses. The state has been among the early presidential contests since only 2008. On the Republican side, it voted twice, in 2008 and 2012, for Mitt Romney, whose Mormon faith made him a good match for Nevada, with its large and politically engaged Mormon population.
In 2012, the state helped Mr. Romney recover from a stinging defeat in South Carolina at the hands of Newt Gingrich. Mr. Romney rallied support in Nevada to blunt Mr. Gingrich's momentum, even collecting an unexpected celebrity endorsement a few days before the caucuses.
The man who gave that endorsement was Donald J. Trump.