Well, the Republicans embody a number of disparate principles, and people tend to focus on a few of them. However, its innacurate to say that there are distinct factions. Rather, there is a sort of continuum between libertarian and conservative Christian ends. People on both ends probably hold many pinions from the other. Note that a lot of the high-profile preachers who talk a good game and pretend they repesent Christians in America have no real power. Fact is, most of the Conservative Christians who are often lambasted as fanatics by Democrats are just honest, everyday people who don’t neccessarily like some aspects of public morals, and often want the government to either conform to them or get out of the business altogether.
The libertarianist segment revolves more about economic issues. They're after making us all rich as kings. They are not really libertarians, for the most part, but contain some strong elements of that school. The Christian wing thinks about what makes a right and good society, and strongly favor canidates they see as honorable or decent.
Now, 'Publicans as a whole tend to be hawks, in the sense that we favor a strong military and an aggressive (not always military) engagement overseas. Some people feel uncomfortable with this, and favor pulling in our own borders more. There’s sometimes debate over which one will make us safer, but for now the externalist approach wins out.
There are not many groups within the party that opposed the war, and there are not many (maybe none) that think a UHC plan is a good idea.
By and large the opinion on Lott is that he was a boneheaded fool who deserved what he got. For all that, it was overblown, given the attitudes of such Democrat mainstays like Carol Mosely-Braun.
Not everyone likes the President, but most feel he’s done a good job doing what needed to be done, with the tools he had to work with. The lack of full-blown WMD development was not a major problem, since the real reason for the war was always to set up a secular but democratic society to, basically, make the entire Arab world eat its hat. And most importantly, we believe its something Gore would have botched completely.