The liberal excesses of the 60s & 70s caused the political pendulum to swing back towards conservatism. Regan promoted conservative values that catered to the Christian right. This began a legacy that Regan, Bush Sr. and now Bush Jr. have continued.
Mitt Romney would like to be the next to carry that torch. Previously a moderate Mormon who supported gay unions, stem cell research, pro choice, and other items considered the antithesis of Christian right values, he shifted his position to a much more conservative stance. In fact, he is now much more conservative than the church is on many positions, aligning himself with fundamentalist conservative Christians positions.
There have been some interesting developments in LDS political front that play into this. Utah is known to be the 'reddest" state in the nation, with a stronger approval rating for Bush than any other state. Bush's strong Utah approval has continued despite Bush having dipped to the lowest approval rating in the US of any president since they began keeping records & Cheney with even lower approval ratings.
But this past week the Salt Lake Tribune reported that Utah's LDS approval for Bush's handling of the war has begun to falter with a 20% drop since January ( http://origin.sltrib.com/news/ci_5517138).
At the same time, other developments have occurred that seem to underscore the church's interest in having Mitt Romney be next in line to lead Regan/Bush/Bush Christian-conservative legacy.
The 1st Presidency has invited Dick Cheney to speak at BYU's graduation ceremony. With church member's good will towards Bush eroding, and Cheney's national unpopularity, a outcry is underway with the papers reporting a flood of concern from around the world, with some members asking how BYU could sponsor an administration considered to be "war mongers." But this may be seen as an attempt to solidify political alliances with conservative Christians, who view Romney's religion suspiciously at best, and heretical at worst, but never-the-less remain loyal to the Bush administration.
All of this is occurring just after Cheney's number one aid - Scooter Libby - was found guilty on charges related to questionable tactics used in promoting the Iraq war and covering up/ denying those tactics. Jurists have reported that the evidence points to the funny business going higher that Scooter Libby (Cheney) and also to Bush's adviser, Carl Rove. No doubt this accounts for a large portion of the outcry over the invitation to Dick Cheney.
Additionally, the church has taken a new step that seem to promote Mitt Romney. Their website has began linking to articles on conservative blogs and websites that are known for their political conservatism. The links are to provide clarification over concerns over Romney's religion. This is done, despite the church's official policy of remaining politically neutral. The grayness of this area leaves the church in a tight position of trying to defend Romney's religion without appearing to promote his candidacy. The church must be careful in this area, because if the government perceives them to be promoting a political party or candidate they could loose their tax exempt status, which could cost them hundreds of millions of dollars. When it appeared that Elder Holland was organizing efforts to promote Romney last year, the church quickly denied such involvement ( http://mormon-chronicles.blogspot.com/search?q=holland+dew+romney).
Whether it wanted this or not, the church has found itself in a difficult position. Excited at the prospect of having a Mormon president, the church wants to promote Romney anyway it can. But it's hands are largely tied because of the Church's tax exempt status and can only use indirect methods to promote him. Romney is courting fundamentalist Christians who despise Mormon doctrine. The church's move to invite Cheney (one of only two schools in the country Cheney will speak at) underscores their loyalty to Bush administration and conservative Christian values, but at the price of aligning themselves with an unpopular president who's administration has taken a less-than impeccable approach to justifying a war, and have managed that war poorly. Since courting the Christian Right, Romney's support has dropped from 8% to just 3%.
This is the best chance for the church to present itself to the public since the Olympics. But the path surrounding a presidential election will not be as easy to negotiate.