In a possible eleventh hour twist to the fast-approaching sequestration this week, two of President Obama's most vocal GOP critics are heading to the White House.
"I've been invited over," Sen. John McCain, R-Ariz., told CBS News. He and Sen. Lindsey Graham, R-S.C., will meet Tuesday with the president, the Arizona Republican said, but the terms of the agenda have not been set.
"I would imagine that it probably has a lot to do with immigration and or sequestration, but I was not told the topic of our conversation," McCain said. "I usually talk about what the president wants to talk about."
McCain - who along with Graham is part of a bipartisan gang of eight senators crafting immigration reform legislation - said he's "sure" something productive could come of the meeting, which grew out of the president's calls to them and Sen. Marco Rubio, R-Fla., on the issue last week. Rubio will not attend the meeting.
Both McCain and Graham dealt directly with then-Sen. Obama on immigration reform, and sources say that history played a part in setting up Tuesday's meeting.
The more pressing issue, though, which the White House and aides to Graham say might also come up, deals with the blind, across-the-board sequester cuts expected to carve into the federal budget Friday.
Appearing on CNN's "State of the Union" on Sunday, McCain said he "won't put all the blame on the president" for lawmakers not having come up with a workable alternative to the drastic cuts, but criticized him over a report that came out this weekend saying the idea for the sequester - hatched amid the 2011 debt ceiling gridlock - originated in the White House.
"The president said during the campaign: Won't happen," McCain said Sunday of the sequester. "I said during the campaign, and so did others say: We've got to stop this from happening. The president has now said it was Congress's fault. We know the president wasn't telling the truth about that."
Still, McCain said today he's grateful for the president's invitation.
"I'm encouraged any time the president wants to talk to me and Lindsey [Graham]," he said. "I mean that. I'm very sincere in that desire."
CBS News Chief White House Correspondent Major Garrett contributed.