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.”

A controversy between Arizona Republican Gov. Jan Brewer and President Obama stemming from her confrontation of the president on an airport tarmac stretched into another day, after Brewer released on Friday a copy of the letter she handed to the president in Phoenix.

"We were at the bottom of the list in job creation. Today, we have a balanced budget and were in the top 10 for job creation. I'm proud of that hard-won recovery -- the result of many tough decisions, courage and perserverance," Brewer wrote. "My hope is that while you are here, you will have a chance to see our tremendous results first hand."

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The confrontation on Wednesday got wide media coverage, especially for the Arizona governor's wag of her finger at the president, captured in a photo. Brewer said after the encounter that Obama seemed tense and "thin-skinned," which she attributed to criticism of his record in her book.

Obama dismissed the encounter as being "blown out of proportion" in an interview Thursday with ABC News.

"I think it’s always good publicity for a Republican if they’re in an argument with me,” he said. “But this was really not a big deal."