The pressure is on the rest of the Republican presidential field to knock Mitt Romney down a peg after the former Massachusetts governor sailed to victory in the Nevada caucuses following his big Florida win earlier in the week.

Romney won Nevada by a decisive double-digit margin. The field charges next into a quartet of contests that will either fuel or check Romney’s momentum.

Newt Gingrich, who just two weeks ago looked like the comeback candidate, held an unusual press conference late Saturday night to, among other things, assure the public he is not dropping out and take a series of swipes at Romney.

The former House speaker predicted his chances would improve the longer the race goes on. He predicted that by the Texas primary in April, he might be able to reclaim “frontrunner” status.

“There are some very big differences evolving in this campaign as we move forward,” Gingrich said. “I believe the vast majority of Republicans across the country are going to want an alternative to a Massachusetts moderate.”

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But as Gingrich assailed his rival as “dishonest,” and Rick Santorum and Ron Paul vowed to take their struggling candidacies into the next states, Romney cultivated the image of a general election candidate.

At his victory rally in Las Vegas, Romney took the same approach as he did after the Florida race – utterly ignoring his Republican opponents, keeping his focus on President Obama and polishing his own brand.

“America needs a president who can fix the economy because he understands the economy, and I do, and I will,” Romney said.

Romney said the president should “be apologizing to America,” describing him as a leader who “demonizes and denigrates almost every sector of our economy.” Romney also seemed to be honing his potential general election message, downplaying recent improvements in the unemployment rate as modest and disconnected from the Obama administration’s policies.

“This president’s misguided policies made these tough times last longer,” Romney said.

The former Massachusetts governor in Nevada scored the first back-to-back win of the campaign. His victory cut across virtually every demographic group and builds Romney’s lead in the delegate count, though Nevada is only the first in a string of lesser contests following the first four behemoth primary battles.

The candidates head next into Colorado, Minnesota, Missouri and Maine, though the Missouri election is more of a beauty contest as it doesn’t determine delegates.

Gingrich, defiant and undeterred, vowed to wear Romney down.

The former House speaker held a lengthy press conference after the caucuses to outline the way forward and assure supporters he plans to take his campaign all the way to the convention in Tampa.

Gingrich then proceeded to tear into his GOP rival, describing Romney as a pro-gun control, pro-tax increase candidate who is “fundamentally dishonest” in debates.

“If you can’t tell the truth as a candidate for president, how can the country possibly expect you to lead as president?” Gingrich said.

The candidate said he would not withdraw, calling that idea the “greatest fantasy” of the Romney campaign.

With 71 percent of precincts reporting, Romney was pulling 48 percent in Nevada. Gingrich had 23 percent and Paul had 19 percent, with the race for second too close to call. Santorum, with 11 percent, will place last, Fox News projects.

Nevada offers a modest delegate haul, with 28 convention delegates at stake. Romney led the field going into the race with 87, followed by Gingrich with 26, Santorum with 14 and Paul with four. It takes 1,144 delegates to win.

Romney, who is Mormon, benefited from the state's demographic makeup, with Mormons composing roughly a quarter of the GOP electorate and almost uniformly supporting him.

Gingrich, in accounting for Romney’s victory, said Saturday “it is a very heavily Mormon state.”

Entrance polls also showed Romney crushing the competition among those who value beating Obama in November as the most important quality in a GOP candidate.

The polls showed Romney leading the field by double digits among evangelical Christian caucus-goers. Romney was backed by 48 percent of evangelicals, compared with 27 percent for Gingrich.

With Saturday’s victory, Romney has won a total of three states. The momentum from his earlier New Hampshire win was briefly interrupted when Gingrich pulled off a stunning victory in South Carolina – and when the Iowa GOP called that state’s race for Santorum despite Romney initially being declared the winner.

Back-to-back wins in Florida and Nevada mark a course correction for the candidate as he heads into several states, such as Colorado, that are considered friendly territory for him.

But the rest of the candidates are keeping up the heat. Santorum in particular has made a pointed plea to Republican voters to reconsider the conventional wisdom that the nomination battle is a two-man race between Romney and Gingrich.

“We are not going to win this election if either of these two guys is nominated,” Santorum said Saturday in Colorado. “Let me assure you. We will not win.”

He urged voters to “reset this race.”

Santorum later told Fox News his campaign is looking at Tuesday – with contests in Colorado, Minnesota and Missouri – as “a big day for us.”

Santorum has recently criticized Gingrich for his ambitious, and costly, space exploration plans -- such as his call for a moon base. And he's taken a few shots at Romney for saying earlier in the week he's not concerned about the "very poor" -- a remark Romney has conceded was a mistake.

Paul, meanwhile, campaigned in Minnesota.

Paul stressed Saturday that it’s still early, and said his support has been fairly constant throughout.

“We want to see how competitive we can be,” Paul told Fox News. “There were nine (candidates), there’s only four, and many of them have come and gone.”