that used to be a big portion of the Republican Party, known in the South West as Sagebrush Republicans. We don't really hear that term any more.They used to believe in keeping the government out of the peoples personal lives. I do wonder how many of them moved over to the Libertarian Party.
The Republican Party is not going anywhere. They are not going to allow another party to take over. And our system is really designed, by the current parties, to really only allow 2 major parties. The parties have protected themselves for their own self interest. So that is not going to change unless we have some sort of huge rebellion, which I don't think people are in favor of. That being said, I think that the Republicans really need to have a powerful (in numbers) group within it that is more liberal to pull it the other direction so that it is more moderate so that our country will be less polarizing and politicians can actually get work done.
As there is a Log Cabin Republican Group within the Republicans, I would like to see a Liberal Republicans Group within the Republican Party that emphasized getting rid of government corruption, minimizing costs, and staying out of the peoples personal lives. That might be something that would appeal to Libertarians and Independents. I'm not really sure how many there are in the extreme right so I don't know how many people would be needed in this type of group to balance it out more. I have friends that are Republicans that would support such a group. They don't like seeing their party taken over by extremists.