The survey from the Pew Research Center for the People & the Press, conducted earlier this month, showed Romney the slight favorite among the Republican and Republican-leaning registered voters surveyed. He edged Herman Cain, 23% to 22%, with Newt Gingrich at 16%.
Pew also asked respondents for their view of the Mormon faith. Among all Republicans surveyed, 54% said it was Christian, while 33% said it was not. Those numbers nearly flipped among evangelicals -- 35% said it was Christian while 53% said it was not.
Last month, Romney called on Texas Gov. Rick Perry to repudiate the comments of a Texas pastor and Perry supporter who had expressed the view that Mormonism was a "cult."
Robert Jeffress introduced Perry at a recent gathering of conservative voters by calling him a "a true conservative" and "a genuine follower of Jesus Christ." Jeffress later told reporters that in a race between Perry and Romney, "we ought to prefer a born-again follower of Christ."
Jeffress said he was simply expressing a view held by many, and the Pew survey seems to support that assessment.
And yet, should he emerge as the nominee, there "is no evidence that Romney's Mormon faith would prevent rank-and-file Republicans, including white evangelicals, from coalescing around him," the study found. The Republicans who are most suspect about Romney's faith "are among the most vehement opponents" of President Obama, it said.
Among all non-Mormons questioned in the poll, a slight majority said Mormonism is a Christian faith. But nearly two-thirds said that Mormonism "is very different" than their own religion. Those views are largely unchanged since a similar point in the 2008 campaign.
Those views are "virtually identical" across party lines," the poll said.
The study was based on interviews with 2,001 adults Nov. 9-14, with a margin of error of 3 percentage points.