Texas Gov. Rick Perry tried to salvage his presidential campaign on Tuesday with an unconventional plan to “uproot, tear down and rebuild Washington,” while businessman Herman Cain tried to project a new command of foreign policy one day after giving a response to a question about Libya that suggested he had no grasp of the issues involved.

Former Massachusetts governor Mitt Romney — the establishment front-runner and the man they are chasing in the Republican nomination contest — spent the day in South Carolina, where he continued to draw a contrast not with his GOP rivals but with President Obama.

With just seven weeks before the Jan. 3 caucuses in Iowa, which will begin the nominating contest, the race appears to have tightened. Former House speaker Newt Gingrich (Ga.), buoyed by a string of solid debate performances, has vaulted to the top tier. In Iowa, he is in a four-way statistical tie for the lead with Cain, Romney and Rep. Ron Paul (Tex.), according to a Bloomberg News survey released early Tuesday.

Despite Perry’s ambitious television advertising campaign in Iowa, a state his campaign says he must win, the poll put him in fifth place, with 7 percent support. So with his candidacy on the line, Perry traveled to Iowa to announce a far-reaching government reform agenda that seemed as unachievable as it was bold.

Perry cast himself as a radical change agent and tried to portray his rivals, Romney in particular, as “tinkering-around-the-margins” managerial types. Perry said he would eliminate lifetime appointments to the federal judiciary. And, calling lawmakers “creatures of Washington,” he said he would effectively transform Congress into a part-time institution by cutting congressional salaries and office budgets in half.

“I don’t believe that Washington needs a new coat of paint; I think the whole place needs to be overhauled,” Perry said. “I’m a true believer that we need to uproot, tear down and rebuild Washington, D.C., and our federal institutions.”

Perry said he would champion a constitutional amendment to institute 18-year terms for the Supreme Court, staggered every other year, and said judges would be replaced in order of seniority.

Speaking to supporters at a manufacturing plant in Bettendorf, Iowa, Perry showcased his new ideas to turn around his campaign after a series of damaging debate performances that included a particularly painful gaffe last week in Michigan.

If elected, Perry said, he would privatize Fannie Mae and Freddie Mac and eliminate or restructure the menu of federal agencies.

“I’m unique to the Republican field,” he said. “I’ve never been an establishment figure. I’ve never served in Congress. I’ve never been a part of an administration. I’ve never been a paid lobbyist. My career has been that of a Washington outsider.”

But Perry is not a political novice. He has served in elected office in Texas since 1985, leading the Romney campaign to dub him a “career politician.”

But on the campaign trail, Romney has ditched his Perry attacks, a sign that he considers the Texan less of a threat. During his visit to Columbia on Tuesday, Romney criticized Obama for having what he described as a pessimistic view of U.S. ingenuity and economic ambition.

“Sometimes I just don’t think that President Obama understands America,” Romney said. “Now, I say that because this week — or was it last week? — he said that Americans are lazy. I don’t think that describes Americans.”

Over the weekend, Obama told a group of chief executives at an Asia-Pacific Economic Cooperation forum that the United States is not “hungry” enough in recruiting businesses and that “we’ve been a little bit lazy, I think, over the last couple of decades.”

Romney addressed about 150 supporters on the floor of a commercial sign factory here. “I’m convinced that America is not lazy, is not soft, has not lost its ambition or its inventiveness,” he said. “I’m convinced that America has all those attributes or more, but that they’re being held down today by a government that’s too big, that thinks it knows more than it does, and that needs to be replaced by people who fundamentally believe in American principles and the American future.”

In Iowa, Rep. Michele Bachmann’s campaign released a new Web video showing her rivals compromising their conservative credentials — Romney’s past comments on abortion rights, Gingrich’s public service ad with then-House Speaker Nancy Pelosi (D-Calif.), Perry’s comments on illegal immigration. The video ends with a new slogan: “No Surprises 2012.”

Cain, meanwhile, found himself on the defensive as he campaigned across Iowa on Tuesday. In an interview with the Milwaukee Journal Sentinel’s editorial board on Monday, he gave a vague, and at times incomprehensible, answer to a question about Obama’s handling of the conflict in Libya.

“My overriding philosophy relative to national security and foreign policy is an extension of the Reagan philosophy, peace through strength — peace through strength and clarity,” he told supporters in Dubuque. “We need to clarify our relationship with friends and enemies around the world and make sure we stand with our friends.”

Henderson reported from Washington. Staff writers Aaron Blake in Dubuque and Perry Bacon Jr. in Washington contributed to this report.

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