I'd rather the Democrats moved left, because "center" is now so far right-wing, it's almost off into the ocean.
Moderate Republicans used to mean people like Howard Baker. Maybe Lincoln Chaffee is a moderate, but who else? Olympia Snowe, maybe.
I'm afraid my definition doesn't fit the current crop of "moderate" Republicans. No, I don't want the Democratic party to evolve into wishy-washy centrism. {Hillary, I am talking to you here. Take note. Go make cookies or something.}
I think the alliance with evangelicals, at least certain ones, has cost the GOP. The Bush voters in Ohio liked the idea of someone standing for their definition of morality. What they got was huge debts, kids killed in Iraq, job losses, home foreclosures, bankruptcy, high health costs, and very little to show on the morality front.