Mr. McConnell’s proposal would essentially flip the current process on its head by calling on Congress to disapprove rather than approve an administration request for a debt limit increase. It would then allow the president to veto the disapproval if it clears Congress, allowing the debt limit to be raised to avoid a default, assuming the veto could be sustained.

The plan also calls for a special Congressional commission to be created that would recommend future spending cuts and policy changes that lawmakers and the White House could then show to the financial markets as evidence that the government intended to get its fiscal problems under control.

Officials knowledgeable about the talks say that the Senate leaders are also negotiating a package of spending cuts that would be attached to the McConnell plan, though perhaps not until it reaches the House. That package would reduce discretionary federal spending by $1.1 trillion over 10 years, take about $200 billion out of programs like federal pensions and agricultural subsidies and save another $200 billion in interest payments.

In order to limit the ability of conservative Republicans to filibuster the McConnell measure, the plan could be attached to a resolution on deficit cutting being considered in the Senate, saving some time given the approach of the Aug. 2 deadline set by Treasury for raising the ceiling.

The bill would still face multiple procedural challenges. And even if it were to pass and create the new process for approving the debt limit increase, Congress would still have to engage in another round of votes on the disapproval of the debt limit increase and a likely veto. But approval of the initial legislation would trigger immediate approval of a $100 billion increase in the debt limit to forestall a crisis should the disapproval and veto process not be complete by Aug. 2.

Since the biggest problem facing the legislation right now is the resistance of House Republicans, the Senate leaders are planning to let the House add the spending cuts into the package as a way to draw support. Even if nearly all House Democrats agreed to back the proposal to avoid a default, dozens of Republicans still must support it to get it across the finish line.

Republicans officials, far from confident that the McConnell plan could clear the House, suggested Monday that the spending package being put together in the Senate might not be enough to win over Republicans who have insisted on a dollar of cuts for every dollar of increase in the federal debt limit.