Under McConnell’s proposal, the president would send a request to Congress for a series of debt limit increases that would have to be offset with spending reductions elsewhere. Congress would be allowed to vote on a resolution of disapproval that would kill the increase, but the president would be able to veto that resolution. Congress then would have to come up with a two-thirds supermajority to prevent the debt ceiling from increasing. A provisional $100 billion would be immediately added to the debt ceiling at the time of the president’s first request to avert default this August while the potentially time-consuming procedural back-and-forth with the White House began.

First, however, Congress would have to pass a bill that sets up the votes and resolutions of disapproval, putting Republicans on the hook for voting for that additional $100 billion in debt.

McConnell’s push to have three votes on raising the debt ceiling before 2012 could be rejected by President Barack Obama, given that the president has said he will not sign any deal that does not extend past next year’s election. But an agreement on a three-vote strategy could satisfy Obama’s requirement that a plan be in place to increase the debt ceiling during that time frame.

Lawmakers are pushing up against an Aug. 2 deadline to raise the debt ceiling but have been insisting on finding a larger deal to also reduce the deficit. With both parties digging in on their priorities — Republicans on taxes and Democrats on entitlements — talks on a larger deal to cut trillions over the next decade have reached a stalemate.

According to GOP aides, McConnell was wary of another agreement that resembled the deal struck by Obama, Speaker John Boehner (R-Ohio) and Senate Majority Leader Harry Reid (D-Nev.) in April to avert a government shutdown. The deal was touted as saving $38 billion from current-year spending, but the Congressional Budget Office ultimately scored the bill as saving only $350 million through September.