I agree with Jamelle Bouie that while Mitt Romney’s RomneyCare problem may be surmountable, his additional Mormon problem may not be:
This is very different from conservative evangelical hostility toward Catholics, which dissipated in the 1970s and 1980s (for a taste of old-school fundamentalist anti-Catholic rhetoric, read a Chick tract). Catholics, at the very least, shared key doctrines with evangelicals. Mormons are in a different boat entirely, and Romney will have to overcome that prejudice to win the nomination, given the evangelical stranglehold on Republican grassroots operations.
To put a slightly more precise spin on this, I think Romney has less of a “Mormon problem” than he does a “Christian problem.” Specifically, it’s very important to a lot of American Christians that other people be Christian. The media is dominated by secular people who aren’t invested in this sort of thing, and tend to accept at face-value the idea that Mormonism is one of several Christian denominations, but a great many Christians disagree with this diagnosis. After all, it’s part of the essence of Bible-based Protestantism that the Bible doesn’t have a sequel. The Catholic church says that Mormon baptisms are invalid and United Methodist Church says “that the LDS Church is not a part of the historic, apostolic tradition of the Christian faith.”
At any rate, if you look at David Thomas Smith’s research (PDF) you can see that attitudes toward Mormonism were a huge driver during the 2008 campaign:
Using Pew data from 2007 which asked questions about attitudes toward Mormonism and toward Mitt Romney, I find that the belief Mormons are not Christians plays a very important role in the formation of general anti-Mormon attitudes, and that while this belief is most widespread among evangelical Christians, it has the same importance in attitude formation toward Mormons even for individuals who are not Christians. The effect of the “Christian question” remains significant but decreases in importance when applied to more politically concrete questions—whether the respondent would be more or less likely to support a Mormon presidential candidate, and how the respondent feels about Mitt Romney. However, more generalized feelings about Mormons are the single most important factor in evaluations of Romney, even more so than party identification or ideology.
All that said, I think it’s unwise to write anyone with some substantial base of support off. That’s because the Republicans generally do winner-take-all primaries, which makes for very unpredictable outcomes in a multi-candidate field.