Editor's note: This story was updated at 6:02 p.m.

In the first real sign of bipartisan progress on raising the nation's debt ceiling, Senate Majority Leader Harry Reid decided this afternoon he would support a plan aimed at cutting up to $3 trillion in debt.

But even though Reid, a Nevada Democrat, has found acceptance with the plan Senate Minority Leader Mitch McConnell spoke optimistically about earlier in the day, he still has a sales job to do with his fellow Democrats. That may end up being a tough sell considering the potential hit on social spending programs long embraced by his party.

According to reports of the deal, the debt limit would increase anywhere from $2.7 trillion to $3 trillion in exchange for a two-stage cut in the federal deficit. In the first, about $1 trillion in spending would be targeted for cuts now while the remaining cuts would be established by a special bicameral panel. If Congress failed to pass the cuts recommended by that committee, then cuts would automatically take place to Medicare and defense programs.

Earlier Sunday, McConnell said that Congress and the White House are “very close” to a debt deal. On CNN”s State of the Union program this morning, the Kentucky Republican said GOP leaders and the White House have “made dramatic progress” toward agreeing on a deal that would reduce the federal deficit by $3 trillion over the next 10 years. In return, the debt ceiling would be raised.

Saturday night, Reid, a Nevada Democrat, postponed a scheduled 1 a.m. Sunday vote on his own debt reduction plan, one that would have raised the ceiling, made spending cuts, and prevented another bruising fight over the debt ceiling until after the 2012 elections. Reid set a procedural vote for early this afternoon to see if he had enough support to limit debate on that proposal. That effort failed to achieve the necessary 60 votes, making the bipartisan compromise the best chance at resolving the debt crisis.

“There are many elements to be finalized, and there is still a distance to go before any arrangement can be completed,” Reid said before the vote on his own plan. “But I believe we should give everyone as much room as possible to do their work.”

Hope for a deal revived Saturday after a partisan start to the day. After the Senate defeated the House approach to lifting the debt ceiling Friday night, the House voted down Reid’s version Saturday afternoon.

“If there’s a word that would right here that would sum up the mood, it would be relief. … default is far less of a possibility now than it was a day ago," Senate Charles Schumer, a New York Democrat, said today on State of the Union.

The White House's face on the Sunday talk show circuit, senior adviser David Plouffe, added a note of caution. "We don't have a deal," Plouffe said. Appearing on ABC's This Week, Plouffe said it wasn't clear if House Republicans would go along with the Senate's move.

Early Sunday, this is how Politico is describing the compromise product in the Senate:

The proposal builds on elements of a House-passed bill credited with saving $917 billion over the next 10 years and raising the ceiling by $900 billion in two increments that should carry the government through the end of this year.

In the interim, a new joint committee would be charged with coming up with an estimated $1.5 trillion in additional deficit reduction, less than targets set in the House measure but still judged sufficient to match Treasury’s remaining borrowing needs to get though the 2012 election year.

[President Barack] Obama is not guaranteed that he will get the full combined $2.4 trillion debt increase that has been proposed, but he would avoid the recurring threat of default next winter if the committee fails to meet its target.

Instead the proposal calls for severe across-the-board cuts as the action-forcing device—cuts impacting Democratic domestic priorities including Medicare but also about 50% from defense spending—a major priority for many Republicans. The goal is to give both parties an incentive to avoid a deadlock in the committee, and the administration will also have a major stake since success will make it easier to manage its borrowing.

The time is running out for Congress and the White House to act. On Tuesday, the nation's debt will exceed it's $14.3 trillion ceiling, creating the possibility for the United States to default on its bills for the first time.

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Kent Hoover is the Washington bureau chief for bizjournals.