"What is it about it (the minimum wage) that drives you Republicans crazy? What is it about working men and women that you find so offensive?" -- Ted Kennedy (D. - Massachusetts)
To the first question, a great many people brighter than I have taken stabs at it, but it boils down to this: The minimum wage reduces the number of available jobs at the low end of the pay scale, hurting the people that the raise in the wage is purported to help.
The really funny thing about it is, the people who call for raises in the minimum wage actually do understand the concept of people buying less of a thing if it costs more. This, of course, is where the calls for $X/gallon gasoline come from, to try to convince people to drive less. Now, maybe they can't bring themselves to accept that a person's labor is a product just as gasoline is, but it works out the same in the end.
It's the second question that really gets my goat, though. Setting aside the fact that, were I a good fiscal conservative, I'd probably sell the goat, there's something about this blatant attempt at class warfare that rubs me wrong. Probably something to do with the fact that I am one of those working class folk.
Now, I'll grant you, there are Republicans out there who think that way. At the same time, though, I have no doubt that such sentiment crosses party lines quite readily. And, just as undoubtedly, there are people out there of all persuasions who have no beef with working folk just for being working folk whatsoever.