TAMPA, Fla. – Republican elders said Sunday that this week’s Republican National Convention here in Florida offered Mitt Romney an opportunity to re-introduce himself to voters heading into the height of the fall campaign season.

As GOP heavyweights gather in Florida for a hurricane-shortened convention, some of the party’s most influential voices laid out on “Meet the Press” the stakes for Romney.

The convention offered Romney a chance “to reconnect with people,” said former Florida Gov. Jeb Bush (R) of the forthcoming convention.

Convention organizers canceled Monday’s activities due to safety concerns associated with an impending hurricane, leaving Romney and the GOP with one less day to drive its message about what they charge are the failures of President Barack Obama, particularly when it comes to matters of the economy.

But Republicans also acknowledged that Romney must use this national platform to reverse some of the damage done to his personal reputation over the summer. The Obama campaign and Democratic super PACs have spent tens of millions of dollars on television ads in key swing states taking aim at Romney’s private sector career, personal wealth and handling of issues important to women.

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Exacerbating problems for the Republican brand has been this past week’s uproar over Missouri Senate candidate Todd Akin’s (R) comments about “legitimate rape.” Republicans have sharply distanced themselves from the conservative congressman’s remarks, while Democrats have sought to link those sentiments with Romney and the Republican Party as a whole.

“I'm surprised that we, the Romney-Ryan ticket, are neck and neck in the polls right now particularly with some of the setbacks we have experienced,” said Arizona Sen. John McCain, the GOP’s 2008 presidential nominee.

Jewel Samad / AFP - Getty Images

Republican presidential candidate Mitt Romney and his wife Ann arrive at the Church of Jesus Christ of Latter-Day Saints in Wolfeboro, New Hampshire, to attend Sunday services on August 26, 2012.

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Convention organizers have laid out a daily theme here in Tampa meant to soften Romney’s public image and offer greater insight into his family and charitable work, among other personal details. The convention also revolves heavily around leveling an indictment of Obama’s economic policy during the last four years.

It’s a high-stakes act for Romney; the conventions are regarded as one of the few opportunities to sway undecided voters, whose numbers are dwindling in this especially competitive election.

“This is the big Etch A Sketch moment for Mitt Romney,” Florida Rep. Debbie Wasserman Schultz, the chairwoman of the Democratic National Committee, said Sunday of the impending Republican festivities.

But there are also long-term stakes for Republicans this week in Tampa, particularly as it relates to closing the gap among women and Hispanic voters, with whom Obama enjoys a healthy advantage over Romney in the polls.

“My personal view is that we need to move beyond where we are,” Bush said of the current Republican rhetoric on immigration. He said that, on immigration, Republicans must change “not necessarily the core of our beliefs but the tone of our message and the intensity of it.”

But Arizona Gov. Jan Brewer (R), the chief proponent of a tough immigration law in her home state, said Republicans must emphasize “the rule of law.”

She added: “Certainly those kinds of issues are going to have to be discussed moving on into the future.”

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But Republicans overall stressed the primacy of the economy this election cycle, the issue on which Romney has an advantage over Obama in most polls.

“I think Mitt wins when it's about these big things,” Bush said. “When it's about the constant distractions, it'll be a very, very close race.”

Arizona Gov. Jan Brewer (R) endorsed Mitt Romney for president during her appearance Sunday morning on “Meet the Press.”

Brewer said she viewed Romney as the most electable candidate to challenge President Obama this fall, and that she made her conclusion after meeting with the candidates and after a debate this week in Arizona.

“I have decided that I am going to publicly endorse Mitt Romney. I think he's the man that can carry the day,” Brewer said. “I think Mitt is by far the person who can go in and win.”

Brewer has become a national figurehead for efforts to curb illegal immigration after leading an effort to install one of the nation’s toughest immigration laws.

She also drew headlines for a confrontation recently with President Obama on an airport tarmac. She was photographed wagging a finger at the president after greeting him and handing him a handwritten note. Brewer described the exchange as being driven by Obama’s dissatisfaction with her book, though the president described the exchange as being “not a big deal.”

Romney is seen as the leader in Arizona, the winner of which is awarded all of the state’s delegates to the Republican National Convention this summer.

Forty-three percent of likely Republican primary voters said they intend to vote for Romney in a NBC News/Marist poll released midweek; he was followed by former Pennsylvania Sen. Rick Santorum at 27 percent, former House Speaker Newt Gingrich at 16 percent and Texas Rep. Ron Paul at 11 percent.

Arizona hosts its primary, along with Michigan, on Tuesday. A larger group of states host their primaries or caucuses a week later, on Super Tuesday. Brewer said she expected Super Tuesday to largely end the battle for the nomination, even if Santorum were to continue fighting.

“He might be in it but I think it’ll be overwhelmingly decided after Super Tuesday,” she said.

That poll also suggested that a Republican candidate who might embrace Arizona’s tough laws targeting illegal immigrants would fare better among primary voters. Brewer was the most vocal proponent of the law, which requires police officers to check the citizenship papers of people they stop or arrest if the officer suspects the person may be in this country illegally.

Sixty-seven percent of likely Republican primary voters said they would be more likely to support a candidate who backs that law, while 25 percent said it would have no effect. Six percent of Republicans said a candidate’s support for the law would make it less likely to win their vote.

Moreover, the poll found that 24 percent of Arizona Republicans said Romney best represents their views on immigration, while 20 percent said Gingrich, and 18 percent said Santorum.