"Mormonism is a big handicap to him," Oman said. "I don't see any way that a Mormon politician can successfully woo evangelical voters who have a strong religious aversion to Mormonism."
In the 2008 race, Romney "had a hard time selling himself as a hard-core conservative," Oman said. "Once he put that on the table, his particular flavor of religion became important."
Of course, any change to his image could revive charges of flip-flopping that Romney ran into last time, because he was a moderate on many social issues when he won the Massachusetts governor's office in 2002.
"The question is, how many times can you reposition yourself before you look like a phony," Oman said, noting a new focus on the economy would be "much closer to the real Mitt Romney than Mitt Romney, the cultural warrior."
Matthew Wilson, a professor at Southern Methodist University in Dallas who specializes in religion and politics, said reinvention is a bigger problem for Romney than religion.
"I think Romney has basically said about all he can say about Mormonism. He addressed it head-on in the last presidential election," Wilson said. "The bigger danger for Romney is if he appears to be reinventing himself yet again."
He said the effect of Romney's faith has been exaggerated.
"The biggest reservation people have about Mitt Romney is the perception he's too slick and doesn't really stand for anything," Wilson said. "More than being a Mormon, he's got to fight against being seen as shifty."
But Kirk Jowers, head of the University of Utah's Hinckley Institute of Politics and a longtime Romney backer, said turning the focus away from religion just makes sense.
"Everyone knows he's a Mormon," Jowers said.
And history is on Romney's side. When the Boston businessman first ran for office against Democratic Sen. Ted Kennedy in 1992, his faith was used to help defeat him. By the time Romney finished running the 2002 Winter Games in Salt Lake and returned to Massachusetts to run for governor, though, his Mormonism no longer mattered to voters.
"It was a complete non-issue," Jowers said. "So the hope for Romney supporters is whatever religious confusion that may have cost him votes in 2008 will be mitigated by 2012."
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