Put simply, House Republicans are demanding new spending cuts - possibly through changes in Social Security and Medicare benefit formulas - as a scalp, and they're dead set against raising more revenues through anything less than an overhaul of the tax code now that Obama has won higher taxes on the wealthy.
"Now the focus turns to spending," Boehner said after Tuesday's vote, promising that future budget battles will center on "significant spending cuts and reforms to the entitlement programs that are driving our country deeper and deeper into debt."
Obama is just as adamant on the other side, saying higher revenues have to be part of any formula for further diverting the automatic spending cuts.
While conservative activist Grover Norquist gave Republicans a pass on violating his anti-tax pledge with this week's vote, he and other forces on the right won't be so forgiving on any future effort to increase revenues.
The refusal of Republicans to consider additional new taxes is sure to stir up resistance among Democrats when they're asked to consider politically painful cuts to so-called entitlement programs like Medicare. Democratic protests led Obama and Boehner to take a proposal to increase the Medicare eligibility age off the table in the recent round of talks.
The upshot? More scorched-earth politics on the budget will probably dominate the initial few months of Obama's second term, when the president would prefer to focus on legacy accomplishments like fixing the immigration problem and implementing his overhaul of health care.
The relationship between Boehner and Obama has never been especially close and seemed to have suffered a setback last month after the speaker withdrew from negotiations on a broader deficit deal. The two get along personally, but politically, a series of collapsed negotiations has bred mistrust. The White House has the view that Boehner cannot deliver while the speaker is frustrated that matters brought up in his talks with the president are not followed through by White House staff.
And on the debt limit, Boehner and Obama at this point are simply talking past each other.
"While I will negotiate over many things, I will not have another debate with this Congress over whether or not they should pay the bills that they've already racked up through the laws that they passed," Obama said after the deal was approved.
Said Boehner spokesman Michael Steel: "The speaker's position is clear. Any increase in the debt limit must be matched by spending cuts or reforms that exceed the increase."