The discussions are scheduled for the day the $85 billion in across-the-board cuts in domestic and defense spending are to take effect.
It will be the first meeting between the president and congressional leaders on the cuts -- known as sequester -- after weeks of finger-pointing from both camps created a scenario in which an agreement on how to avert the sequester might not be reached, The Washington Post reported Wednesday.
Last week, Obama called congressional leaders.
Expected to attend Friday's meeting are House Speaker John Boehner, R-Ohio; House Minority Leader Nancy Pelosi, D-Calif.; Senate Majority Leader Harry Reid, D-Nev.; and Senate Minority Leader Mitch McConnell, R-Ky.
While both sides agree that agree that an alternative to the sequester is necessary because it would devastate the still-recovering and fragile economy, they have conflicted over whether new tax revenue should be part of the equation, which Obama and Democrats want but Republicans don't.
Both sides also have accused the other of employing scare tactics to frighten the public. While Republicans say Obama came up with the idea of the sequester, Democrats note that it passed Congress with bipartisan support.
Senate Democrats and Republicans were expected to submit opposing proposals to resolve the sequester Thursday, but neither was expected to get the votes needed to pass, the Post said.
While the sequester begins Friday, its effects won't be felt for several weeks as the cuts are implemented.
Also looming is the expiration of a stopgap funding measure to keep the federal government operating. The continuing resolution expires at the end of March.
A Republican aide pounced on Obama and the timing of the meeting.
"If the president is serious about stopping the sequester, why did he schedule a meeting on Tuesday for Friday when the sequester hits at midnight on Thursday?" the aide, who declined to be named, told the Post. "Either someone needs to buy the White House a calendar, or this is just a belated farce. They ought to at least pretend to try."