President Barack Obama will meet Tuesday at the White House with Republican Sens. John McCain of Arizona and Lindsey Graham of South Carolina to discuss immigration changes, a White House official said.

McCain has complained in previous years that Obama dropped the ball on the issue — after one meeting at the White House early on in his presidency. McCain and Graham are the senior Republicans in the “gang of eight” that is pushing the immigration effort.

Obama has also reached out to members of the group by phone in recent weeks, and the White House has said repeatedly that the president hopes the Senate can hash out a bipartisan bill on the issue.

McCain and Graham also have been among the harshest critics of the president’s foreign policy, particularly the handling of the terrorist attack in Benghazi, Libya, and the nomination of former Sen. Chuck Hagel as secretary of Defense. The Senate will vote Tuesday on overcoming a filibuster of Hagel’s nomination.

Graham, meanwhile, signaled an interest again in reaching a broad budget deal, telling CNN that he was open to $600 billion in new revenue if Democrats agreed to entitlement cuts.