Congressional leaders met at the White House yesterday for yet another discussion, and this one didn’t quite last an hour. No progress was made towards finding an agreement that would end the Republicans’ hostage standoff, but the gathering lasted just long enough for President Obama and Treasury Secretary Tim Geithner to look ahead to what happens on late Sunday afternoon.

Specifically, Obama and Geithner explained that the possibility of a panic in the global markets was becoming quite real. Asian exchanges will open on late Sunday afternoon, and to stave off the first wave of a disaster, a viable plan would have to be announced beforehand.

House Speaker John Boehner (R-Ohio) told his caucus he hopes to meet this deadline, and presented a new approach.

By early evening, the outlines of a two-stage strategy were emerging. First, lawmakers would vote on a package to cut agency spending by as much as $1 trillion over the next decade and raise the debt limit, currently set at $14.3 trillion, by the same amount. That would give Geithner enough borrowing authority to cover the nation’s bills through the end of this year.

Then Congress would go to work to produce as much as $3 trillion in additional savings through an overhaul of the tax code and major changes to Social Security and Medicare, the biggest drivers of federal spending. To identify those savings, Congress would create a new bipartisan debt-reduction committee comprising 12 lawmakers from both the House and Senate, an idea offered by Senate Majority Leader Harry M. Reid (D-Nev.).

In the same call, Boehner reportedly ruled out the possibility of passing the McConnell/Reid “Plan B” solution, citing widespread opposition to the fix among House Republicans.

While Democratic leaders are reportedly open to resolving the crisis in two steps, there’s a sticking point. Oddly enough, it’s not about revenue — it’s about the size of the debt-ceiling increase.

Under Boehner’s latest strategy, the first phase would be an agreement for about $1 trillion in cuts (with no revenue) accompanied by a debt-ceiling increase of the same size. But it would be a temporary fix — once this is complete, a new series of negotiations over tax reform and entitlements would begin. The hope would be to craft some kind of compromise early next year, at which point, Congress would have to raise the debt ceiling again.

Democrats see this as untenable. They can live with accepting $1 trillion in cuts with no revenue now, followed by a second round of revenue/entitlement cuts, but want one vote on raising the debt ceiling, not two.

Why? A couple of reasons. One, it’s bad enough for the economy to have this kind of crisis now; knowing that we’ll have to do it again next year would create widespread uncertainty and run the risk of undermining the economy event more. Two, getting Congress to approve a debt-ceiling increase is hard enough; trying to get this done in an election year exacerbates the risk and makes the threat that much more serious.

But Republicans, as usual, don’t want to compromise. As a result, we’re no closer to a resolution.

Senate Majority Leader Harry Reid (D-Nev.) said in a statement last night that he’s “deeply disappointed in the status of negotiations” and urged Republicans “to reconsider their intransigence.”

Talks among party leaders are expected to resume, at some level, this morning.

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Steve Benen

Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.