David Jackson

USA TODAY

LAS VEGAS — Donald Trump swept to victory Tuesday in Nevada's Republican caucuses, a third consecutive win that he said would likely propel him to the Republican presidential nomination.

"A couple of months ago we weren't expected to win this one," Trump told shouting supporters at the Treasure Island casino, also citing his previous triumphs in the South Carolina and New Hampshire primaries. "Of course, if you listen to the pundits, we weren't expected to win too much — and now we're winning, winning, winning the country."

Predicting victories in upcoming primaries, Trump said: "It's going to be an amazing two months ... we might not even need the two months."

Marco Rubio took a small lead over Ted Cruz for a distant second, while Ben Carson and John Kasich were well back in single digits.

Speaking with his supporters in Las Vegas, Cruz said he is the only "consistent conservative" candidate left who can beat Trump.

As caucuses were ongoing, reports emerged of problems at some locations.

Voters and journalists in Nevada on social media noted problems at several caucus sites, including organizers wearing Trump and Rubio gear, a lack of ballots, late starts, long lines, and the fact that ballots included the names of 11 candidates, including candidates who have dropped out of the race.

The Nevada Republican Party tweeted that "there have been no official reports of voting irregularities or violations" at caucus sites. It also said it is not against the rules for volunteers at caucus sites to wear campaign gear.

Rubio, appearing at a casino in Las Vegas early Tuesday morning, reminded backers to look up the locations of their caucus sites: "Make sure you know exactly where to go tonight — it's that important."

The Florida senator later left Nevada, before the caucuses began, to campaign in Minnesota and Michigan.

It appeared to be another record Republican turnout in Nevada, just as in the previous GOP contests in Iowa, New Hampshire, and South Carolina.

The win puts Trump in a commanding position ahead of 11 state delegate contests next Tuesday.

Polls of caucus goers in Nevada indicated an angry Republican electorate, many of whom went for Trump because they want an "outsider" for their candidate. GOP voters concerned with the illegal immigration issue also strongly backed Trump.

In recent days, Rubio and Cruz spent as much time fighting each other in Nevada as the front-running Trump, though there are signs that is changing.

Rubio appeared to refer to Trump when he told supporters in Vegas that "being angry is not a plan," and voters should not go for "the loudest person in the room."

Cruz, who has argued for days that Trump is more liberal than conservative, told Nevada backers Tuesday that the billionaire's views "change every day" with the political winds.

During a rally in Sparks, Nev., earlier Tuesday, Trump called Cruz a liar who engaged in dirty tricks, and warned supporters to look out for "dishonest stuff" during the caucuses.

As for his other major rival in Nevada, "I've been very nice to Rubio, because he hasn't hit me. When he does, you will see what happens."

Marco Rubio doesn't need an outright win ... for now

The caucuses followed a difficult moment for Cruz. On Monday, the Texas senator fired his communications director Rick Tyler over social media postings of an article making the false claim that Rubio mocked the Bible. The Texas senator, who has been criticized by Trump and Rubio for questionable campaign tactics, said Tyler made "a grave error."

Speaking with reporters, Rubio said that Cruz made Tyler the "fall guy" for a campaign culture of dirty tricks that Cruz embodies. Trump told backers at a Las Vegas rally on Monday that Cruz is a liar and added that "this guy is sick — there's something wrong with this guy."

On Tuesday, Trump tweeted that Cruz "panicked" and was "disloyal" to his spokesman.

Rubio, who narrowly edged Cruz for second place in South Carolina, entered the caucuses with endorsements from high-profile Nevada Republicans, such as Sen. Dean Heller. The Florida senator told voters in Las Vegas that "I'm a conservative who can unite this party" ahead of the fall election after a fractious primary process.

Cruz, meanwhile, said he was the only Republican candidate who can beat Trump, having done so in the Iowa caucuses on Feb. 1, while Rubio has not won anything.

Cruz, who has attacked Rubio as being weak on immigration, also raised the stakes on that issue in Nevada, vowing to deport an estimated 12 million people who are in the country illegally. Rubio has described that idea as expensive and impractical.

Both Rubio and Cruz are seeking to be the sole alternative to the front-running Trump, though there are no indications that any other candidates plan to drop out.

Carson, the retired neurosurgeon, told supporters after the Nevada caucuses that "I believe things are starting to happen here," ahead of next week's contests.

Kasich, the governor of Ohio, has spent most of his time campaigning in states that vote next week and month. He was in Georgia on Tuesday

Supporters who turned out to see Trump in Las Vegas on Monday said they like his attacks on the government and that he is a businessman who is financing his own campaign.

Mercedes Fenyves, 45, a family caretaker from nearby Boulder City, said Trump may sometimes be "harsh," but "his being able to speak his mind overshadows everything." Fenyves said she is having trouble making ends meet, and the struggling middle class needs things to change.

Lynn MacFarlane, 57, a Las Vegas businesswoman who attended a Cruz event, said Trump "flip-flops" too much for her taste, while Cruz is a "consistent conservative."

Elections 2016 | USA TODAY Network