I'm a practicing Mormon. I'm also a registered Democrat, which really puts me in the minority. However, it also demonstrates that the LDS church belongs to neither political party, nor does the church dictate to its members what to believe. In fact, the church has always taken a strictly neutral political stance, the most obvious reason being it would lose its tax-exempt status. While congregations are always encouraged to vote, participate in local government, and volunteer in civic affairs, the church leadership does not endorse a particular candidate or viewpoint. The only exception that I'm aware of was in 2000 when the church president, Gordon Hinckley, urged California mormons to vote for the referendum against same-sex marriage. But I and many other mormons disagree with Hinckley on this issue, which we are free to do without any repercussions. In church we talk a lot about being a "quiet example" to non-Mormons in our actions. Usually this inolves mundane things like helping someone with a flat tire or volunteering at the library. While some of us are zealous in sharing our beliefs with others, most of us keep quiet about it. This is partly because mormonism is so mysterious to most people, and partly because religion just isn't discusssed much in public.
Generally, mormons are quite socially conservative. Most of my mormon friends believe in the right to bear arms, that this is a Christian nation that has been hijacked by godless liberals, that abortion should be outlawed and gay marriage is wrong. They put priority on the family -- which means they don't let their kids watch R-rated movies and discourage drug abuse, not that they support healthcare for children or more child-care for working moms. They watch Fox News and love Rush Limbaugh.
However, I don't think Romney would champion social conservative issues if elected. Judging from his famously shifting views on gun control, universal healthcare, gay rights, same-sex marriage, and abortion, it seems Romney doesn't really have strong feelings either way. He appears to be a CEO-style candidate, who will say and do what is expedient to get the job done. He appears to be first and foremost a businessman, not a Mormon beholden to Salt Lake City.
fryde67's comment about an "oath" to the church is ludicrous. While it is true that faithful members do pledge to give their time, talents and energy to the LDS church (not on pain of death), that is as broad as leaders pledging to uphold the Constitution. Bush, Pelosi, Scalia, Waxman -- all believe they uphold the Constitution with their actions. There's lots of wiggle room there. Come on: Romney is a multi-millionaire who gives most of his time now to campaigning -- he doesn't spend much time devoted to his current job as governor, let alone give it to the church. No one expects him to donate even half his wealth to the church.
Regarding religious issues, I think President Romney would be even less interested than Bush in "faith-based initiatives" and opening the door to the Christian right. So far he hasn't worn his religion on his sleeve -- indeed, it seems reporters bring it up, not him. Mormons today are trying to shed the insular, exclusive culture that used to exist and become more involved in our communities as ordinary citizens with individual views. I think Romney is that kind of mormon.