— Texas Gov. Rick Perry spent the weekend in this early-voting state trying to revive a campaign damaged by shaky debate performances and to lure back Republicans turned off by his views on immigration and Social Security.

At a series of traditional political stops across southern New Hampshire — including three town-hall forums and a house party — Perry touted his record of job creation as Texas governor. He forcefully defended his support of in-state tuition for certain illegal immigrants. And he accused those who claim he wants to dismantle Social Security of “scare tactics.”

“No one up there on that stage has a stronger record than I do when it comes to illegal immigration,” Perry told a rain-soaked crowd in Manchester, pushing back against the narrative that his support for the Texas DREAM Act makes him too soft on immigration for the Republican Party’s most stalwart conservatives.

Perry, who rocketed to front-runner status shortly after declaring his bid for the Republican presidential nomination seven weeks ago, has since been weakened by those perceptions as well as his unsteady appearances in three nationally televised debates. He has been out-muscled by the better-funded, better-organized operation of his chief rival for the nomination, former Massachusetts governor Mitt Romney.

Even speculation over the past week about whether New Jersey Gov. Chris Christie would jump into the race has been viewed in some quarters as a vote of no confidence in Perry’s potential to challenge Romney from the right, as many had hoped he would.

Whether Perry made headway during his two-day New Hampshire tour remains to be seen. He told one crowd that he is boning up on economic matters by consulting with former presidential candidate Steve Forbes, and he was scheduled to work on debate preparation with policy experts on his drive to the Manchester airport Saturday afternoon.

He catered to conservatives with promises to abolish the federal Energy and Education departments and a pledge to hire an administrator of the Environmental Protection Agency “who is not there to make any friends.”

But Perry drew moderate crowds of 150 or so and only polite applause with his most pleasing lines, notably when he said the evidence is not “incontrovertible” that climate change has been caused by man. He did not win over everyone with his explanation that the Texas DREAM Act was a “Texas solution” — not necessarily for every state.

“I don’t understand why any governor would give preferential treatment to the child of somebody who does not belong here rather than these guys here or his grandchildren,” said Dave Connors of Hampton, pointing to those seated around him as he addressed Perry at one event. “It doesn’t make sense.”

Even at Perry’s own events, Romney’s superior organization was in evidence; on Friday in Derry, Romney supporters handed out phony Perry jobs plans filled with empty pages (along with Romney’s own 160-page plan). And on Saturday, the roads leading to one of Perry’s town halls were festooned with dozens of Romney yard signs (which two young Perry supporters worked feverishly to remove).

“I’m really right in line with Perry’s principles,” said Kevin Kimball, 53, of Hampton, who works in human resources and attended Perry’s first town hall of the day. Like many who attended, Kimball is not thrilled with Romney’s moderation, notably his support for a health-care overhaul in Massachusetts that served as a model for President Obama’s plan.

“But I don’t think Perry’s quite as polished as Romney,” Kimball said. “He's got to get better.”

Perry also caused a stir at his final tour stop by saying that he would consider sending U.S. troops to Mexico to fight drug violence.

“It may require our military in Mexico,” Perry said in answer to a question about drug violence along the southern border. In the back yard of New Hampshire gubernatorial contender and tea-party activist Ovide Lamontagne, Perry offered no details, and a spokesman, Robert Black, said afterward that Perry would work with the Mexican government. But Black declined to specify whether Perry is amenable to sending troops into Mexico with or without the country’s consent.

“If he were president he would do what it takes,” Black said.

The remarks prompted speculation about exactly what Perry meant and what the implications might be for the nation’s relationship with Mexico.

The issue also opens the door to scrutiny of Perry’s position on U.S. military intervention generally. The governor has criticized Obama’s management of military operations in Afghanistan and elsewhere; on Saturday, at the same campaign appearance where Perry made his remarks about Mexico, he promised never to send troops into another country without a detailed plan for winning and withdrawing quickly.

Pressed to explain Perry’s remarks, Black, the spokesman, offered this: “Never say never. Mexico has a problem. They have a significant problem with drug cartels at war with each other. And that is a significant problem for the United States.”