Republican presidential candidate, Texas Gov. Rick Perry speaks during a campaign stop at Joey's Diner, Tuesday, Nov. 29, 2011, in Amherst, N.H. (AP Photo/Jim Cole) (Jim Cole/AP)

The up-in-the-air Republican presidential contest edged into a new phase Tuesday as the candidates returned to the campaign trail with the kind of urgency that accompanies this reality: In just five weeks, voters will begin to have their say.

The aspirants took their messages directly to voters across the crucial early voting states — Mitt Romney was in Florida, Newt Gingrich in South Carolina, and Rick Perry and Jon Huntsman campaigned across New Hampshire.

Businessman Herman Cain gave an evening speech in Michigan, despite saying earlier in the day that he was “reassessing” his campaign after the allegation Monday that he had an extramarital affair.

In a campaign that has been dominated by a series of nationally televised debates, the candidates sought to sharpen their pitches in more intimate settings and build momentum heading into the Jan. 3 Iowa caucuses that kick off the nominating contest.

“This is that point where everyone can see the finish line, and all of a sudden, the candidates start to sweat,” Republican strategist Alex Castellanos said. “We’re in Act Three — the big battle — and it’s the beads of cold sweat. The geometry gets a lot more complicated now.”

In an unpredictable race of booms and busts, the one constant near the top has been Romney. Yet he, too, was looking for a new edge. He campaigned in Miami amid boxes of guava bites and cans of coconut water, trying to ingratiate himself with Florida’s politically powerful Cuban American community. The confident Romney declared to the Democrats, who have begun attacking him on a regular basis: “Bring it on.”

But the former Massachusetts governor has never been the candidate of the moment. At this moment, that’s Newt Gingrich, who cut the ribbon at one of five new campaign offices in South Carolina — a symbolic gesture of his changing fortunes.

In a late-day interview on Fox News, Romney lodged his first attack on his surging rival, labeling Gingrich “a lifelong politician” and suggesting he lacks credibility on economic issues.

Asked by Fox News’s Bret Baier whether Gingrich could beat President Obama, Romney said: “I think to get President Obama out of office, you’re going to have to bring something to the race that’s different than what he brings. He’s a lifelong politician. I think you have to have the credibility of understanding how the economy works. And I do.”

Rick Perry, meanwhile, journeyed to New Hampshire in search of a rebound that could get him back into a race. The Texas governor campaigned with an Arizona sheriff known for his harsh stance against illegal immigrants, but the Texas governor’s slip of the tongue at a town hall meeting — he suggested that the legal voting age is 21, not 18 — was a fresh reminder of his struggles.

Romney: ‘Bring it on’

During a pair of campaign stops in Florida on Tuesday, Romney tried to highlight his private-sector experience and business know-how, sticking to themes that have become staples of his stump speeches. And though he kept his focus exclusively on Obama, some of his swipes might also apply to Gingrich and Perry, who have long careers in elected office.

“What concerns me today as I watch Washington and people who spend all of their lives in politics there, is some of them don’t understand the nature of America,” Romney said at a rally in Miami.

Romney, who picked up endorsements from a trio of powerful Cuban American politicians, seemed confident and controlled. He delivered short, crisp speeches in his necktie and slacks. He invited his youngest son, Craig, on stage to say a few words in Spanish.

Romney’s events were carefully choreographed, and the candidate took no questions — until he looked into a sea of supporters and found a reporter asking him about the Democratic National Committee’s latest attack ad against him.

Romney used his answer to press his campaign’s argument that the Democrats fear him more than any of his Republican rivals.

“It shows that they’re awfully afraid of facing me in the general election,” Romney said. “They want to throw the primary process to anybody but me, but bring it on. We’re ready for ’em.”

Trying to project mastery

Gingrich tried to show that he is just as ready, predicting that Obama would run a campaign of “astonishing dishonesty” and would win only if he presents himself as “less disgusting” than the Republican nominee.

At a town hall meeting, the former House speaker spoke for well over an hour, answering every question with adverbs — “fundamentally . . . astonishing . . . utterly . . . radically” — that left his audience convinced he had mastered the issues.

At an outdoor mall near Hilton Head Island, he talked about how to build a fence along the southern border, how to rebuild the Environmental Protection Agency and the Department of Education, and what’s wrong with Obama’s health-care overhaul.

This was the second day of a three-day swing across the Palmetto State, where Gingrich, who once represented a district in neighboring Georgia, has drawn big crowds. He wore a pin representing the Revolutionary War battle flag of Gen. George Washington and told his audiences about its historical significance.

Gingrich, who has been rising in the polls over the past few weeks in part because of strong debate performances, is positioning himself to take advantage of Cain’s troubles.

People of a certain age

It’s the debate performances that have left Perry’s campaign as almost an afterthought. Perry tried to make up ground Tuesday by talking about immigration, an issue where his moderate record has hurt him with conservatives, and campaigning with a new supporter: Joe Arpaio, sheriff of Maricopa County, Ariz.

But Perry may have undercut the effort to get back on track with another gaffe.

“Those who are going to be over 21 on November 12th, I ask for your support,” he told college students at a town hall meeting. “Those who won’t be, just work hard.”

Neither age nor date will be particularly pertinent for Perry. The voting age is 18, and the 2012 election will be held Nov. 6.

Speaking to a small coffee-sipping breakfast crowd, Arpaio called Perry an “honest and ethical” man who had taken action to help secure Texas’s border with Mexico.

Arpaio joined Perry again at a town hall meeting at the New Hampshire Institute of Politics at St. Anselm College, where Perry pledged to detain and quickly deport all illegal immigrants apprehended in the country and to secure the border with Mexico within a year of taking office.

“I have been a law-and-order governor,” he said, “and I’m going to be a law-and-order president.”

Gardner reported from South Carolina and Helderman from New Hampshire.