LAS VEGAS » With a big win in Nevada, Donald Trump claimed a third straight commanding victory in the race for the Republican presidential nomination. Marco Rubio edged out Ted Cruz in a tight race for second that offered little evidence that Republicans were ready to coalesce around one strong alternative to the businessman billionaire.

With victories now under his belt in the West, the South and Northeast, a gleeful Trump was oozing even more confidence than usual Tuesday night that the GOP nomination is within reach.

“It’s going to be an amazing two months,” he told a raucous crowd at a Las Vegas casino. “We might not even need the two months, folks, to be honest.”

Trump’s rivals know they are running out of time to stop his juggernaut.

Rubio edged out Cruz by fewer than 2,000 votes, according to The Associated Press vote count.

Appearing today on NBC’s “Today” show, Rubio said the majority of Republicans don’t want Trump to be their nominee for president. “The sooner we can get this race narrowed, I think the easier it’s going to be to stop Donald Trump, he said.

After finishing third in Iowa, fifth in New Hampshire and second in South Carolina and Nevada, Rubio needs a win soon to support the idea he can beat Trump.

Cruz, for his part, skipped right past Nevada’s underwhelming verdict for him in his caucus-night speech and pinned his hopes on the big round of voting that’s coming up next, saying: “One week from today will be the most important night of this campaign: Super Tuesday.”

The candidates were fanning out to their next targets of opportunity as the lights went out in Las Vegas: Trump was campaigning today in Virginia, then on to Texas and Oklahoma. Rubio and Cruz both headed for Texas.

Entrance polls in Nevada captured the sentiment propelling Trump’s insurgent campaign: Six in 10 caucus goers said they were angry with the way the government is working, and Trump got about half of them.

Cruz, a fiery conservative popular among voters on the GOP’s right, had finished a disappointing third in South Carolina after spending much of the past two weeks denying charges of dishonest campaign tactics and defending his integrity. Nevada raises more questions about his viability.

But Cruz harked back to his win in Iowa’s leadoff caucuses to remind supporters that his is “the only campaign that has defeated Donald Trump is this campaign.”

The election calendar suggests that if Trump’s rivals don’t slow him by mid-March, they may not ever.

Trump won 14 delegates in Nevada, while Rubio won seven and Cruz got six. John Kasich and Ben Carson each got one, with one delegate left to be allocated.

Overall, Trump has 81 delegates, and Cruz and Rubio have 17 apiece. Kasich has six delegates and Carson has four. It takes 1,237 delegates to win the Republican nomination for president.

Trump, in his victory speech, took on the notion advanced by both Rubio and Cruz that if more GOP candidates drop out of the race, they’ll coalesce around an alternative.

“They keep forgetting that when people drop out, we’re going to get a lot of votes,” he said.

Nevada’s caucusing played out in schools, community centers and places of worship across the state — a process that’s been chaotic in the past.

Count Tracy Brigida, fed up after her husband was laid off from his mining job, among those caucusing for Trump.

“I want a businessman to run the biggest business in the world,” Brigida said as she caucused at a Las Vegas high school.

Jeremy Haight drove straight from his marketing job to caucus for Marco Rubio at the same high school.

“He’s the most level-headed. He hasn’t said anything stupid or crazy … which is really what I think the country needs,” Haight said.

It was Cruz for Megan Ortega, who declared: “He’s consistent, he’s bold and he’s a class act.”

Preliminary results of the entrance poll found that about 3 in 10 early caucus goers said the quality that mattered most to them in choosing a candidate was that he shares their values, slightly more than the quarter who said they want a candidate who can win in November. About a quarter said they want a candidate who can bring change. About 2 in 10 want one who “tells it like it is.”

Trump — no surprise here — was supported by nearly 9 in 10 of the “tell it like it is” voters.

Lagging far behind in the Nevada vote were Kasich and Carson.

The entrance poll survey was conducted for The Associated Press and the television networks by Edison Research as Republican voters arrived at 25 randomly selected caucus sites in Nevada.

Benac reported from Washington.