Democrats should push the ideas that the Bush is supporting the anti-gay marriage amendment to distract from the deficit, Iraq and jobs.
They should also challenge his sincerity about passing the amendment. Use the amendment to create a wedge between the GOP and Right Wing religious extremists.
The Democrats should point out that if Bush were really attempting to pass the amendment, as opposed to milking it for votes in an election year, gay Republicans like Jim Kolbe and Mark Foley would probably quit the GOP. If they aren't quitting, you can infer they've been promised this will go away after the election.
Also, Democrats should push for a vote on the amendment soon. The votes aren't there to send this amendment to the states, not because there is no Dem support but because there is Republican opposition. Dems should then point out issues like tax cuts for the wealthy where Bush was able to line-up unanimity (or pretty close) in the GOP Congressional delegation. Dems should then point out that Bush and the GOP places a higher priority on tax cuts for rich people than on "social conservatism".