It's gimmicky, but the House GOP passed their suspension of the debt limit law for 4 months, thus allowing the Treasury to spend beyond what had previously been authorized.

Washington Post:

But even as House Republicans voted to suspend enforcement of the debt ceiling through May 18, their budget chairman vowed to use the coming deadlines to force President Obama and Senate Democrats to deliver "a big down payment on the debt crisis."

"Spending cuts are coming," House Budget Committee Chairman Paul Ryan (Wis.) told reporters at a breakfast hosted by the Wall Street Journal. "We are not going to lose the $1.2 trillion we've already got from the last debt-ceiling [fight]. We are going to have to negotiate on top of that for a new debt-ceiling increase. . . . We're very serious about this."

He and other House leaders rallied GOP support for Wednesday's debt-limit vote by promising to deliver a budget plan that would wipe out deficits within the next decade - a daunting task. For the past two years, the House has passed budgets that propose to cut spending far more deeply than Obama and other Democrats are willing to accept, and even those austere frameworks would take nearly 30 years to achieve balance.

Meanwhile, Ryan ruled out the possibility of lowering deficits by raising taxes, as Democrats prefer. The "fiscal cliff" deal approved this month would generate about $650 billion in new tax revenue over the next decade. That, Ryan said, is enough.

"They got their revenue increases already," he said.

Ryan's hard-line position on the budget appeared to reassure House Republicans, who voted overwhelmingly for Wednesday's debt-limit measure. It passed on a vote of 285 to 144, with 33 Republicans voting no.

Republican leadership will tread carefully over the next few months, balancing the need to keep their base happy and appear to be cooperating enough with Democrats on budget talks. While the meat cleaver cuts in sequestration appear certain to be enacted, once the pink slips start going out, it is likely that some kind of deal will be reached.

Cutting specific dollar amounts may be emotionally gratifying but unthinking, across the board cuts are self-defeating. The key will be to hold Democrats to cutting one dollar for every dollar restored from sequestration. That may prove difficult, but Democrats are as anxious as Republicans to avoid the worst effects from sequestration and may be more pliable down the road.