During the meeting, which will happen the same day the so-called sequester will take place, the president and lawmakers are also expected to discuss the next looming fiscal showdown, a March 27 deadline to continue government operations or face a government shutdown.
On Capitol Hill, there's a lot of finger pointing about the upcoming $85 billion in cuts of 5 percent to domestic agencies and 8 percent to the military.
Little to no progress has been made so far between House and Senate leaders and the White House, and given the hard feelings engulfing Washington, there's no guarantee that this problem can be solved, even though the stakes - a shutdown of non-essential government programs after March 27 - carry more risk than the across-the-board cuts looming on Friday.
The sequester will have a wide-reaching impact, including on national parks and recreation areas. More than 400 of them have submitted contingency plans to cut 5 percent of their budgets in case Congress can't find a solution to the sequester.
The Santa Monica Mountains National Recreation Area is one place preparing to make difficult choices. On the chopping block are deferred maintenance, like roads, buildings and sewage systems; a reduction in youth programs, which would eliminate outdoor educational opportunities for 6,000 children; and volunteer programs.
"Because we have limited staffing to manage those volunteers, we expect that we'll lose about 4,000 volunteer hours, which has about an $86,000 benefit to the parks, so that would also be a big loss," said Kate Kuykendall, a spokeswoman for the recreation area.
Commercial air travel could also pay dearly if sequester cutbacks become a reality.
"We'll be unable to land on all four runways, for instance, if we don't have certain positions open. If we can't run at all four runways, you slow the arrival rate down. That means you're waiting wherever you're at instead of being in the air flying to Los Angeles," said Michael Foote of the National Air Traffic Controllers Association.
The air traffic controllers union isn't alone in spelling out widespread problems that could be caused by the budget impasse. The secretary of transportation and the head of the Federal Aviation Administration issued a joint statement:
"As a consequence of employee furloughs and prolonged equipment outages resulting from lower parts inventories and fewer technicians, travelers should expect delays. Flights to major cities...could experience delays of up to 90 minutes during peak hours," the statement said.
Twenty-three small airports in California could see their air traffic control facilities closed, places like Hawthorne Municipal Airport and Santa Monica Airport. LA/Ontario International Airport will lose its overnight shift in the control tower.
The Transportation Security Administration says it too will have to furlough workers, which will likely lead to even more delays at checkpoints.
A new ABC News-Washington Post poll found a majority of Americans disapprove of the way the president and congressional Republicans are handling federal spending, but Republicans got the worst marks.