Conservatism seem to revolve around three central ideas. One of the ideas is economic conservatism, the idea that we deserve what we earn unless it was taken by force, theft, or fraud. The second is national security conservatism, the idea of taking threats to our country seriously and being pro-active in dealing with them, as Reagan was during the Cold War and as Bush was when we launched a War on Terror that sent us into Iraq. This, I suspect, doesn't mix terribly well with economic conservatism, since war is expensive, and the money for guns and tanks probably can't be got from bake sales. And then there is social conservatism, the use of the government attempting to uphold traditional values, leading to anti-abortion/gay marriage positions. The last two increase the involvement of government. If government is out there trying to stop abortions fighting enemies, this has to be paid for.
It would be fair enough to ask if liberalism goes together as well. I suppose we could say liberals accept
1) The proactive role of government to alleviate poverty and its consequences.
2) Restraint in fighting against supposed threats to our country (not going into Vietnam or Iraq).
3) Upholding a strong doctrine of the separation of church and state, not attempting to bring the state into controversial question of value.