Sure they will, with plenty of votes to spare.
I read a Reuters story yesterday that said the bill only needed some "moderate" Republicans to join the rats in the House for passage. The problem Boehner has is that he can't bring a bill to the floor for a vote and let it pass mostly by Democrat votes. That would show the party base that the rats can run roughshod over the GOP with barely a fight. Boehner and the Republicans would look like complete fools, and Boehner would be doomed as Speaker.
I don’t know. A bill as presently spoken about, which might include spending cuts to be re-sent to the Senate, would gain no support from the Dems. Let’s wait for the final bill and then we can judge.