Friday's meeting, the first face-to-face one since Obama was sworn in for his second term in January, essentially looks past the cuts to the next looming fiscal crisis: a possible government shutdown at the end of March.
In Washington's stormy partisan atmosphere, the annual ritual of passing agency spending bills collapsed entirely last year, and Congress must act by March 27 to prevent the partial shutdown.
Economists and lawmakers alike agree that the cuts, the potential shutdown and the country's series of fiscal crises overall are hurting the country's shaky comeback from the Great Recession, and the effects will be felt around the world. Both political parties have said the cuts — of 5 percent to domestic agencies and 8 percent to the military— could inflict major damage to government programs and the economy at large.
Obama, speaking to a group of business executives Wednesday night, said the cuts would be a "tumble downward" for the economy, though he acknowledged it could takes weeks before many Americans feel the full impact of the budget shrinking.
White House spokesman Jay Carney said Friday's talks are designed to be a "constructive discussion" about how to keep the deep spending cuts from having harmful consequences.
The spending cuts to defense and other programs had been designed to be so ugly that Washington would be forced to avoid them and come up with a better way to tackle the country's $11.7 trillion debt. But the warring sides in Washington have spent this week assigning blame rather than seeking a way out.
There is breathing room, however, for political settlement if Friday's deadline comes and goes. Many of the cuts to hit the Defense Department and other federal agencies would come in later years and could be partially offset by cuts in programs that are wasteful or behind schedule.
But the need to keep the government's doors open and lights on — or else suffer the first government shutdown since 1996 — is immediate, and it requires the Republican-dominated House and the Democratic-controlled Senate to agree.
In the latest session of Congress, the least productive since World War II, they rarely have.
Republicans are planning for a vote next week on a bill to fund the day-to-day operations of the government through the Sept. 30 end of the 2013 fiscal year — while keeping the new $85 billion in cuts in place.
The Republican plan would award the Pentagon and the Veterans Administration with their line-by-line budgets, for a more targeted rather than indiscriminate batch of military cuts, but it would deny domestic agencies the same treatment.
And that has whipped up opposition from Democratic senators. Domestic agencies would see their budgets frozen almost exactly as they are, which would mean no money for new initiatives such as cybersecurity or for routine increases for programs such as low-income housing.
"We're not going to do that," said Sen. Tom Harkin, a Democrat. "Of course not."