Anchored by Jake Tapper, The Lead airs at 4 p.m. ET on CNN.
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In a closed-door meeting with House Democrats Wednesday, President Barack Obama said he would agree to a short-term debt limit increase if Republicans were on board, according to a Democrat who was in the meeting.
If such a bill were to pass, it would probably last just six weeks.
Obama and Speaker of the House John Boehner will come face-to-face Thursday. The president invited the entire House Republican caucus to the White House, but the speaker declined, and said only GOP leadership will attend.
A House Republican told CNN that the Republicans will push for a short-term extension to the debt limit, and will not be talking about reopening the government.
"I don't understand it, frankly. It gets us off our crisis footing this week, but we're going to be back on a crisis footing at Thanksgiving, or sometime," said Independent Senator Angus King, of Maine.
"I don't think the debt ceiling ought to be the subject. I think it's perfectly appropriate to negotiate budget issues in connection with the budget, and the continuing resolution, and the funding. But the debt ceiling we ought to just do and move on, in my view," said King.
If the president is willing to do a short-term extension, and the Republicans agree, it will likely happen, to King's disappointment.
"That's more of what we seem to do best around here, which is put things off," said King.
Angus was a two-term governor of Maine, who ran against a Democrat and a Republican. There had been a shutdown in Maine two years prior, and Angus campaigned against the partisan system.
Angus, who caucuses with the Democrats, said while the last two weeks in Washington have been awful, his first nine months in town showed bipartisan promise in negotiations over student loans and immigration.
"But the problem is you get into this budget stuff and the Affordable Care Act, and you're getting to the core values of the two parties. And that's the hardest thing of all to make a deal," said King.
The Independent senator was spotted on the Senate floor recently talking to tea party-supported Sen. Ted Cruz, R-Texas.
"I went over and sat down with Ted because I wanted to know – can we move beyond this Obamacare thing?" said King. "His answer was no."
Democrats gave King a hard time for talking to Cruz at all.
"It does have a seventh grade quality to it," said King.
But King pointed to a sign of hope from Congressman Paul Ryan.
By penning a Wall Street Journal op-ed offering his view of how to get out of this mess – a solution that did not once mention Obamacare – Ryan offered what King called "a wilted olive branch."
King said he has met with about 15 senators, from both sides of the aisle.
"Everybody's trying to figure out how do we get ourselves out of this fix. The focus, a lot of the conversation is how do we help John Boehner get himself out of the fix that he's in," said King.
For more of our interview with Sen. Angus King, watch the video above.