President Obama will meet with congressional leaders Friday at the White House to discuss a way to avoid the fallout of deep spending cuts – around the time they are technically set to begin, officials said Wednesday.

Weeks of finger pointing on both sides have not led to an agreement to avoid the cuts, known as the sequester. The meeting will be the first between Obama and congressional leaders on the issue.

House Speaker John Boehner (R-Ohio), Senate Majority Leader Harry Reid (D-Nev.), House Minority Leader Nancy Pelosi (D-Calif.) and Senate Minority Leader Mitch McConnell (R-Ky.) are expected to attend.

Shortly after the meeting was announced, McConnell said Republicans would work with the president, but only to replace the sequester with other spending cuts. He reiterated Republicans' opposition to Obama's central demand of higher tax revenues.

"The message my constituents keep sending is simply this: Replacing spending cuts that both parties have already agreed to and which the president has already signed into law with tax hikes is simply unacceptable," McConnell said. "[Obama] wasn't elected to work with the Congress he wants. He was elected to work with the Congress he has. That means working with both parties to get things done. . It means leaving the gimmicks behind and working with us to hammer out a smarter solution to his sequester."

"We’re still ready to work with them to get something responsible done," McConnell said. "But we can’t do it alone."

Obama has said the $85 billion in cuts to domestic and defense spending would have a devastating impact on the government and harm the economy. Republican leaders agree that an alternative to the sequester is necessary.

But the two sides have clashed over whether new tax revenue should be part of the solution. Senate Democrats and Republicans on Thursday are expected to advance dueling proposals to resolve the sequester, but neither is expected to get the votes necessary to pass.

The sequester technically begins Friday, but the effects won’t be felt for several weeks, as they are implemented. Federal furlough notices are likely to be among the first steps the government takes.

Both sides are hoping to resolve the battle by late March, when a stopgap measure funding the government expires.

Boehner spokesman Michael Steel said that the meeting with the president was scheduled for the day after the sequester is slated to begin.

"At this point the Obama administration isn't even pretending to try to stop the sequester," Steel said.

ABC News first reported the expected meeting this morning.

Rosalind S. Helderman and Ed O'Keefe contributed to this report.