It's not about the Republicans needing anything to pass, it's the Democrats who need things to pass. With the White House and the Senate, they can set the agenda, but only if they get the House to go along. Despite that, Boehner has set the price for GOP cooperation to zero. That's not any kind of strategy, it's outright surrender.
I think the surname “Boehner” is French? IF so that would explain the fall down strategy.