Lowering taxes is (in theory) a forcing function to reduce the size and control of the federal government. The republicans want a small government for a few key reasons:
1) Lower taxes reduce the burden on the people who are the most productive.
2) Smaller government requires people to fend more for themselves than in some more socialized states, ultimately making them more productive.
3) A smaller government is less intrusive on individual liberties and rights (similar to the libertarian point of view, but less extreme)
4) Conservatives are big on state control, so you shouldnt need as large of a federal government.
5) They're also big on the idea that the government does things less efficently than the private sector, so you should push as much to private industry as possible, keeping it out of government.
What we've seen recently is that theory and reality are pretty different, and cutting taxes does not constrain congresses ability or willingness to spend, and we just get ourselves into a load of debt and end up with big government anyway.