President Obama has extended an invitation to top congressional leaders to huddle at the White House on Tuesday, three days out from the deadline by which Congress must hammer out a budget deal for the rest of the fiscal year or else see the government shut down.

White House Press Secretary Jay Carney announced the planned meeting at his daily media briefing Monday. The participants will include Obama, House Speaker John Boehner (R-Ohio), Senate Majority Leader Harry Reid (D-Nev.), Senate Appropriations Committee Chairman Daniel Inouye (D-Hawaii) and House Appropriations Committee Chairman Hal Rogers (R-Ky.).

“The president has made clear that we all understand the need to cut spending, and significant progress has been made in agreeing that we can all work off the same number, $73 billion in spending cuts in this year alone,” Carney told reporters Monday. “With the process running short on time, the president will urge leaders to reach final agreement and avoid a government shutdown that would be harmful to our economic recovery.”

The $73 billion figure cited by the White House is a reference to Obama’s proposed budget, which was never enacted; the actual cuts being considered would trim $33 billion from current spending levels.

Asked whether Obama is confident that a shutdown can be avoided Friday, Carney told reporters that the president “remains confident that if we, together, roll up our sleeves and get to work, very quickly, that we can find a compromise that reduces spending by $73 billion, protects the investments that are so key to our future economic growth, allowing us to out-innovate, out-educate and out-build the rest of the world, yes, he believes that can get done.”

Carney noted, however, that “time is of the essence,” pointing to Obama’s calls over the weekend to Reid and Boehner, a rare personal intervention by the president in the talks he had previously left to Vice President Biden and Office of Management and Budget Director Jacob J. Lew.

Democrats have insisted that tentative agreement has been reached on the $33 billion figure and that the issue is now whether to make those cuts from non-defense discretionary spending (as Republicans would like) or from a broader universe that includes mandatory spending programs, such as those inside the departments of Agriculture and Treasury.

Republican leaders, who face pressure from their right flank to push for the deepest cuts possible and also include controversial policy riders in any final budget deal, have disputed that any agreement has been reached on a number.

The slated White House meeting also comes on the same day that House Budget Committee Chairman Paul Ryan (R-Wis.) is set to unveil House Republicans’ proposed budget for the next fiscal year.

Staff writer Perry Bacon Jr. contributed to this report.