Obama's meeting with the two U.S. senators, part of a bipartisan "Gang of Eight" working to craft immigration legislation, was described by a White House official on Monday as focused on that issue.
But a McCain aide said the White House encounter likely would go beyond immigration and could include the looming $85 billion in government spending reductions that will hit domestic programs and the Pentagon unless a last-minute deal is reached.
The White House escalated a campaign on Monday to convince Americans dire consequences await if the so-called "sequester" cuts go ahead on March 1, warning of a slowdown in global trade, a stalled fight against cancer and compromised border security.
But there was no word that Obama was ready to start negotiations. Graham is a member of Senate committees on appropriations and the federal budget. He and McCain both sit on the armed services panel. The McCain aide said the U.S. troop drawdown from Afghanistan could also be discussed on Tuesday.
The planned meeting marks Obama's latest outreach to some of the Republicans involved in negotiating an overhaul of the U.S. immigration system.
Facing criticism for not getting more involved in the delicate process on Capitol Hill, Obama phoned McCain, Graham and Senator Marco Rubio last week. It was not immediately known why Rubio, a rising Cuban-American star in his party and considered crucial to winning conservative backing for any reform deal, was not scheduled to participate on Tuesday.
Obama backs the Senate reform effort but he and the Republicans differ over some key details.
Obama emphasized in his recent State of the Union address the importance of creating a clear path to citizenship for the estimated 11 million immigrants in the United States illegally.
Many Republicans stress that there must first be measurable progress in securing U.S. borders, a condition hard for the president to accept if it drags out the legalization process.
The White House, however, is counting on Republicans feeling pressure to move swiftly on immigration reform after they were chastened by Latino voters' rejection in the November election.
(The story corrects million to billion in paragraph 3)
(Reporting By Matt Spetalnick; Editing by Doina Chiacu)