The White House has told Senate Majority Leader Harry Reid to cut a deal with Sen. Joe Lieberman so that health care legislation could pass, according to the Politico.

Yesterday on CBS’ “Face the Nation,” here’s how Lieberman described his demand:

“You’ve got to take out the Medicare buy-in. You’ve got to forget about the public option. You probably have to take out the Class Act, which was a whole new entitlement program that will, in future years, put us further into deficit. And you’ve got to adopt some of the cost containment provisions that will strengthen cost containment, that all of us favor.”

But if Reid were to make all of those changes (a big if, because it would be contingent on his ability to get liberal Senators to cave), there’s no garuntee that Lieberman would be on board — even though he said so yesterday.

Strip out everything Lieberman said he is opposed to, and Democrats will end up with a bill largely along the lines of the “Baucus bill” that passed through the Senate Finance Committee.

Yet back in October, Lieberman told Don Imus that he couldn’t get behind the Baucus bill. “I’m afraid that in the end the Baucus bill is actually going to raise the price of insurance for most of the people in the country,” he said.

And this is just the headache the White House has in the Senate.

Rep. Raul Grijalva, co-chairman of the 80-member House Progressive Caucus, has told ABC that even with the Medicare expansion, the Senate bill would be “irreconcilable” with the legislation that cleared the House.

UPDATE: The White House is now publicly denying that they are pushing for a deal with Lieberman.