Unless a few RINOs peel off and join the Dems.
If Bush gets his way by getting Dems to vote with him, that alone should show he is on the wrong side of the issue here.
But the question is whether the leadership of the House will call for a vote at all. The practice since 1994 has been that the GOP leadership doesn't even call for a floor vote unless a majority of Republicans are in support. The exceptions you might recall, such as CFR, were forced by petition.