The primary reason the House has been a deal-stopper so far is more because of Boehner's resistance to bring bills to the floor unless they would be supported by a majority of the House Republicans regardless of whether they'd pass a floor vote.

It's assuming (IMO correctly) that it will be too politically difficult for Boehner to prevent the Senate's bill from coming to the floor of the House and being voted on.

In the House vote, it's likely the most conservative House members will still vote against it, but there should be more than enough votes for it to be passed (with the House votes coming from moderate Republicans + all/nearly all Democrats).