Diversity, it seems, is not a thing to be shunned, but a blessing to be embraced. Just ask the church leader. In fact, the Mormon Church regularly reminds their members that gospel principles compatible with the Church may be found in the platforms of the various political parties. And, LDS members are strongly encourage to participate and vote in local, state and national elections.
Nevertheless, a large majority of Mormons tend to lean Republican, and an overwhelming portion of those seem to support Mitt Romney's candidacy. Mormon Democrats, however, do exist. There have been some prominent Mormons who have shared that they were Democrats. The most recent was President James E. Faust of the First Presidency of the Church. Many Mormon Democrats believe that the Democratic Party takes the strongest position on many moral issues. For example, feeding the hungry, clothing the naked, visiting the sick and administering to their relief, both spiritually and temporally are principals espoused by the Church as well as the Democrats. Furthermore, LDS scriptures' insistence that the world and all living things were created spiritually prior to their physical creation calls us to environmental stewardship, another moral issue defended more robustly by Democrats.
Mormon Democrats too often face criticism from fellow believers and are told that their political views are out of step with doctrinal teachings. Yet, being an oppressed minority is nothing new for Mormons. It's how they ended up moving across the continent and setting up the locus of their culture in a desolate wasteland next to a giant lake filled with salt.