Since it's hard to detect Bush's core economic principles it's impossible to say what he'll do. I'm guessing he'll go along to get along. Meanwhile, another thread here on commodity prices points to a downturn in the economy. Tax increases in the face of a downturn would be a disaster.
President Bush won't go along with this. But it's possible for a bill to be passed through Democratic Congress but that means there will be an opportunity for him to veto it.