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But many in the Church are concerned the media will portray their faith unfairly, and an equal amount — 68 percent — say Romney's nomination will bring at least some bad publicity for Mormonism.

A Gallup poll released earlier in the month showed that registered Mormon voters overwhelmingly favored Romney. Some 84 percent of Mormons surveyed in that poll said they would vote for Romney, versus just 13 percent for President Obama. That's a marked improvement over Republicans' already dominant numbers among Mormon voters; in 2008, John McCainJohn Sidney McCainGOP strategist donates to Alabama Democrat Meghan McCain knocks Bannon: 'Who the hell are you' to criticize Romney? Dems demand Tillerson end State hiring freeze, consult with Congress MORE pulled 75 percent of the Mormon vote, versus 19 percent for Obama.

But a separate Gallup poll released last week found that Romney's faith could keep some voters at home. According to the survey, 18 percent of respondents said they would not vote for a Mormon.