Update, 11:46 a.m.: Well that didn't take long. The White House has already rejected Plan B.

Original post: House Speaker John Boehner announced in a press conference Tuesday morning that he's suddenly pushing a Plan B for the fiscal-cliff negotiations, in which the House will stop the Bush tax cuts from expiring January 1 on income below $1 million. He also hopes the backup plan's outline will prod President Obama into a better deal for conservatives. Boehner was briefing his fellow Republicans about the plan Tuesday morning, Politico's Jake Sherman and John Bresnahan reported before the speaker's vague and brief appearance alongside House Majority Leader Eric Cantor. Plan B would detach the Bush tax cuts from the rest of the stuff being negotiated over to avoid the fiscal cliff. While Republicans "continue to have hope that we can reach a broader agreement with the White House," Boehner said, he's offering "a backup plan to make sure as few American taxpayers are affected by this tax increase as possible." Cantor added: "The president is not yet there — he has not yet come to where he needs to be" on spending cuts.

Boehner had already offered to raise taxes on income over $1 million on Friday as part of a larger deficit-cutting package to avoid the fiscal cliff. Obama's counter-offer was to raise taxes on those making more than $400,000 — he'd previously insisted on the $250,000 mark. Obama offered $1.2 trillion in new revenue and $1.2 trillion in spending cuts, and NBC News' First Read said Tuesday morning that the "fact the White House is agreeing to the Boehner principle of 1-to-1 revenue increases vs. spending cuts on this deal means it’s now about exchanging numbers, potentially dotting 'I's and crossing 'T's."

The two are still a bit apart, and Boehner's Plan B is something "leadership sources say they hope this move prods the administration to move toward them," Politico reports.