The move was welcomed by the White House as a signal that GOP leaders are serious about preventing a government default, but it enraged some conservatives who want to leverage the debt-ceiling vote to secure trillions of dollars in spending cuts.
Bipartisan leaders from both chambers, including Pelosi and McConnell, are scheduled to meet with Obama Wednesday afternoon in an effort to break the stalemate — the fifth such gathering in the past week.
The Treasury Department has said it can pay its debt obligations through Aug. 2, after which it will default.
The Democratic reaction to McConnell's proposal has been varied. Some lawmakers — including House Minority Whip Steny Hoyer (Md.) and Rep. Peter Welch (D-Vt.) — have rejected it outright.
"We need to give a sense of certainty, a sense that the Democratic government of the United States of America can work and make decisions, not punt one more time," Hoyer said Wednesday on Bill Press's radio show. "The McConnell proposal is punting one more time."
But other leaders have echoed Pelosi's praise that McConnell has offered a plan to avoid a government default. Senate Majority Leader Harry Reid (D-Nev.) and Rep. Steve Israel (D-N.Y.), for instance, have both said they want to take a closer look at the proposal.
"This does sound to me like kind of a Rube Goldberg contraption," Israel said on MSNBC Wednesday. "But look, we'll look at it, we'll consider it, so long as at the end of the day it leads to a balanced package that doesn't ask the middle class and seniors to fund corporate tax loopholes."
Pelosi on Wednesday said she's optimistic that bipartisan negotiators will still be able to reach an agreement on a much larger package before the deadline, precluding a fall-back plan like McConnell's.
"I salute President Obama for putting forth a grand bargain," Pelosi said from her office, where she was hosting several students to hear their concerns as the debt talks evolve. "It reduces the deficit well into the future, and we should still strive for that — or come as close to it as we possibly can."
Pelosi rejected the notion that the debt talks are stalled, arguing that they have led to the "elimination of possibilities, narrowing the path that we may go down."
"And that's progress," she said.
Some Democrats have grown frustrated with Obama's willingness to accept the demands of GOP leaders during recent budget debates. They say he caved to the GOP when he agreed in December to extend the George W. Bush-era tax cuts to the wealthiest Americans.
Yet Pelosi applauded Obama's receptive approach, arguing that his "unprecedented" openness will ultimately bear fruit in the debt-ceiling talks.
"He is a remarkably patient man," she said, "and I think that that patience will take us to a consensus."