Republican Mitt Romney outlined a deficit-reduction plan here on Thursday that he said would slash federal spending and “economize, simplify and make smarter government.”

With the presidential race focusing for the fourth straight day on businessman Herman Cain and allegations that he sexually harassed three former employees, Romney and other White House hopefuls stumped in New Hampshire and across Iowa, searching for support just two months before Republicans start voting in the nominating contest.

Texas Gov. Rick Perry visited a seed-production company outside of Des Moines, touting his jobs record and signaling that he increasingly views Iowa as the most hospitable place from which to revive his struggling campaign.

The horse race seemed frozen in place as the Cain drama unfolds. But Rep. Michele Bachmann (Minn.) and former senator Rick Santorum (Pa.) barnstormed the Hawkeye State, hoping they, too, might seize any momentum if Cain’s supporters suddenly abandon him.

Here in New Hampshire, where Romney enjoys a big lead in the polls, he presented his prescription for the country’s growing debt. He said he would cut federal spending by about $500 billion during his first term by eliminating programs and services he doesn’t like (he cited President Obama’s health-care overhaul) and those he does like but doesn’t think the country can afford (he cited Amtrak).

Romney also pledged to turn responsibility for costly entitlement programs like Medicaid over to state governments, to “let states draft programs in a way they think best to care for their own poor.” He plans to reveal more details of his fiscal policy agenda during a speech Friday in Washington.

“There’s some who say when you talk about fiscal responsibility and cutting a program, you’re showing that you’re heartless,” Romney added. “We have to say, ‘No, no, no, you have to understand. We have a moral responsibility not to spend more than we take in.’ . . . It is a moral responsibility to believe in fiscal responsibility. We do and I do.”

Romney addressed more than 300 voters and students who stood and sat shoulder-to-shoulder inside the quaint Exeter Town Hall, which was built in 1855 and has survived many a blizzard and even a hurricane. Romney talked for about 20 minutes, delving into wonky budgetary details, and once casually interrupting his thoughts to say hello to a crying baby.

As he began, with his wife, Ann, seated behind him, Romney cautioned that he would not be scripted. “If I stumble around a bit, it’s because I wrote these notes in the automobile,” he quipped. “I can’t always read what I’ve written, but I’m going to do my best.”

The exercise seemed designed to demonstrate that Romney, with more than two decades of private-sector experience, is the only Republican with the business know-how and budget-cutting chops to solve the nation’s debt puzzle.

To reinforce that point, one of his surrogates here, former governor John E. Sununu, stepped up to the podium to pronounce: “You cannot just talk about a fancy tax program . . . This is a man that understands that you don’t just say, ‘Gee, I wish I could cut a budget.’ He knows the decisions are hard, and he knows how to make them.”

Drawing a contrast between Romney and his rivals campaigning in Iowa, Sununu said: “I’m fond of saying Iowa picks corn.” Turning to Romney, he added, “New Hampshire picks presidents.”

At nearly the same hour, Perry was at Pioneer-Hi Bred, a seed-production company in Johnston, Iowa, telling about 150 employees about his plan for an optional flat income tax at 20 percent.

“Would you rather have that?” he asked, pulling out a postcard to illustrate a simplified tax form that he said would “substantively and forever change the IRS.” Or, he added, “stay with the lawyers and the accountants?”

Perry promised to show “up in Washington, D.C., with a sledgehammer” and “crush that system,” referring to what he says is an over-regulated capital city where lobbyists enjoy too much influence.

Meanwhile, Bachmann laid out a tax plan of her own, saying her overhaul would result in fewer tax brackets and lower rates. She said her plan would require all wage earners to pay some income tax, however modest.

During a visit to Iowa State University in Ames, Bachmann invoked former presidents of both political parties, according to the Des Moines Register. She said her economic principles are similar to those of Ronald Reagan, while she quoted John F. Kennedy by saying: “Ask not what your government can do, ask what you can do for your country . . . I hope I got that right.” (Close. Kennedy said, “Ask not what your country can do for you.”)

Santorum continued his whirlwind, week-long tour of the Hawkeye State, which on Wednesday made him the first candidate this cycle to claim the bragging rights of campaigning in each of Iowa’s 99 counties.

But it’s a feat that seems to be bearing little fruit for Santorum thus far. The former Pennsylvania senator is languishing in polls in Iowa and elsewhere. And history is replete with the names of White House hopefuls — John Edwards and Bill Richardson, to name a few — who traversed all 99 counties, only to come up short in the caucuses.