The Democrats are like a guy running around with a torch outside a corral of GOP horses. They wave the torch and see how many are spooked, or, even better, stampede.
What Boehner should do is to simply pass the GOP spending and revenue bill based on the House Budget. Then go home for the holidays awaiting news the Senate has passed their budget and acted on the House bill. Then the normal recon can occur.
To do otherwise is worse than folly for the GOP.