The new line from John Boehner is that the onus is now on the Senate to pass a fiscal cliff solution, and then the House will take up and consider whatever the Senate passes.
On the face of it, this is nonsensical. Democrats have a majority in the Senate. Anything that's acceptable to both Barack Obama and John Boehner will easily get through the Senate. That's why all the negotiations thus far have been Obama-Boehner negotiations, with perhaps a side order of Nancy Pelosi. But while Boehner's proposal is illogical, I understand why he likes the idea.
The reason is that while anything Boehner and Obama agree to will easily pass the Senate, in the absence of an agreement it'll be hard for Obama to get anything past the Senate. He'd need a lot of Republican votes to overcome a filibuster, and those votes would probably come through something like Gang of X talks between Republicans and squishy moderates like Kent Conrad and Joe Lieberman. Conrad wants to split the difference between the President's last offer and Boehner's last offer. Then once something like that difference-splitting bill passes the Senate, Boehner gets to take it up as the new baseline for negotiations and pull the ultimate resolution even further to the right.
But that's exactly why Obama would be foolish to take any such thing seriously. Starting in the New Year, the Senate gets more liberal. The House also gets more liberal. And the policy baseline also gets more liberal. The White House isn't going to pull the plug on negotiations, but unless Boehner comes back to the table with something new to say they have no incentive to further weakn their hand.