John Boehner wants big spending cuts, but he's extremely vague about what those would be:

What does Speaker John Boehner want out of the debt ceiling vote? It’s now unclear, as Boehner is avoiding any specifics, dodging questions three days after calling for “trillions” in cuts.
Here’s a snapshot: In a Thursday briefing with the Capitol Hill press corps, Boehner said he didn’t “want to tie myself down” on budget process reforms, refused to “lock myself into” a time frame for the trillions of dollars in savings he’s seeking. He declined to respond to whether tax increases and offsetting the debt limit hike are completely non-negotiable bargaining positions.

There are two ways for Republicans to get President Obama to sign large spending cuts. One is to strike a mutually-acceptable-deal, which would mean a bargain that raised revenue along with cutting spending. The disadvantage of this approach for Boehner is that he has to meet Obama halfway on the substance. The advantage is that he can obtain Obama's political cover -- because Obama agrees to the deal, he can't attack Boehner for slashing Medicare (and Boehner can't attack Obama for raising taxes).

The other way to get spending cuts is to force Obama to swallow a bill he hates by taking hostages. The advantage of this plan to Boehner is that he can craft the ransom entirely to his liking. The disadvantage is that he can't have Obama smiling in the Rose Garden about how this is a sensible compromise that both sides deemed necessary.

Boehner seems to want to do both -- to force Obama to make concessions by threatening to harm the economy, and to get Obama to cover for him. Because if Boehner is after entitlement cuts, then those cuts will be unpopular. He can demand them, and Obama can let the public have a say as to whether those demands are a good idea.

Obama's play here is obvious. He needs to tell Boehner to write him a bill specifying precisely what he needs in order to approve a debt ceiling increase.