It looks like Boehner is going to call for a vote tomorrow on a one-week budget extension that cuts $12 billion and extends Defense funding for the rest of the year. It's smart because I imagine it will pass the House and then it puts the Senate or less likely the President in the position of saying "no" to something that results in a shut down.
I don't know what I would do if I were in the Senate's or President's place. To meet in the middle, cuts should probably include Defense. After all, Defense is 20% of the budget.
But you can see the clever plan. With each extension, put in for the rest of the year some item the Republicans want until all you're debating are the ideologically driven cuts. So then the Democrats finally get the blame for shutting down the government over NPR or Planned Parenthood, which would not go over well.