The Goldwater Institute has nailed this one perfectly.
Subsidizing politicians with taxpayer money violates the basic principle of keeping government as small as possible. It is an obvious extravagance, not a necessity. Even worse, by doling out the resources that are needed to run for office, the government wields control over the electoral process. This undermines a crucial check by insulating elected officials from the people they represent and rendering them dependent on the government for their political success.
No serious small government conservative or libertarian should want anything to do with government (read: tax payer) funded campaigns. They should run from it whenever it is waved in their faces. Relying on a handout from the taxpayer to gain political power over that same taxpayer is the antithesis of libertarian and conservative beliefs.
Serious conservatives and libertarians should also be doing everything they can to rid our system of these clean elections laws.