I see libertarianism as a tendency in American poltics. The party is the distilled version of it, but the tendency has more impact than the party.
Many of the strategy and tactics around business issues, like regulation, taxes - comes from the libertarian point of view. Reason Magazine's take on drugs and prostitution haven't gained much traction in the GOP, but if you go read their articles about regulations, government agencies, or analysis around specific topics they appear to be setting the mainstream GOP agenda fairly frequently.
The same old conservatism mostly, but for some reason libertarians are trying to erase conservatism from conservative economics.
Libertarianism makes conservative economics and small, limited government, impossible. Only conservatism can return us to limited government.