You are ingnoring two factors, one our favor, and one against. President Bush is a man of his word, he said before he was elected that he would sign an AW Ban renewal. He said it again, through his spokesmen, after he was elected. He tends to keep his word. OTOH, he also is a man of honor who took the "support and defend" oath, and if he can be convinced that the second amendment completely prohibits such a law, he will veto it and explain the reason he didn't do what he said he would. So there is hope he might not sign it, and a victory in the Supreme Court in the Silveira case would go along way to convincing him of it's unconstitutionality. (And even if it didn't, a win in that case would make getting the federal AW ban declared unconstitutional by any number of courts would be a slam dunk as well)
Like he kept his word when he said he would veto the CFR bill?
OTOH, he also is a man of honor who took the "support and defend" oath, and if he can be convinced that the second amendment completely prohibits such a law, he will veto it and explain the reason he didn't do what he said he would.
He cares about as much about the Constitution as his predacessor did. Hell, he hasn't even vetoed a single bill yet. Do you really believe that EVERYTHING Congress has sent him is constitutional?
Anyway, I seriously doubt he has even read the bill and doubt that he could even summarize it's key points accurately. He's simply doing what his political advisors tell him, in this case.
So there is hope he might not sign it
I doubt it. He's as anti-gun as his daddy was. The elites, be they Bushes, Doles, Clintons, or Kennedys, don't like guns in the hands of us peasants.