This post has been updated.

A source close to the discussions between President Obama and Speaker of the House John Boehner (R-Ohio) on the “fiscal cliff” told me Sunday evening that Boehner offered to extend the current tax rates for everyone making less than $1 million, while allowing the tax rate for those making more than $1 million to expire on Jan. 1 as currently scheduled. The terminology here is important because no Republican would technically be voting for a rate increase.

House Speaker John Boehner, left. (J. Scott Applewhite/Associated Press)

Some Republicans  have suggested simply letting the tax rates rise on income of $250,000 and above, leaving spending cuts and negotiations on entitlement for the debt ceiling fight, where House members have greater leverage. Boehner, however,  is wary of giving the president $800 billion in revenue (the amount from letting the rates rise on those making more than $250,000) without spending cuts. He therefore is trying to get protection for those making up to $1 million (which would include many upscale professionals in blue states) along with entitlement reform and spending cuts.

Despite the president’s public chest-thumping, the source suggested that the president in private is showing some flexibility to enact spending cuts. However, no deal is imminent. Moreover, the president might well be content, as many have speculated, to insist on a tax increase for households making more than $250,000 without “paying” for it in the form of spending cuts.

If there is no hope for a deal, House Republicans would have several options, including passing a bill to protect all but millionaires (which might draw some blue-state Democrats) with or without spending cuts and sending it over to the Senate to force Democrats to take a vote.

All of this confirms what some have suspected: By freeing himself from the impossible (the desire to keep all the George W. Bush tax cuts in place), Boehner has much more bargaining room either now or during future debt-ceiling talks. His goal, of course, is to make the GOP the protector of tax cuts for the middle and upper middle classes (everyone making less than $1 million, which excludes most small businesses) while forcing spending cuts (or revealing Obama to be a phony when it comes to spending reduction).

There are two components here that haven’t yet been worked into the puzzle.

What happens to the sequestration cuts, particularly the defense cuts? The president promised in the campaign to take care of these, but so far there seems to be no interest on his part to protect national security from “devastating” cuts. (From the House perspective, these cuts could be reduced or reallocated during a debt-ceiling negotiation.)

Finally, what happens to tax reform? In the original conception of a “grand bargain,” tax reform was meant to be an acceptable generator of revenue. But if, for example, the GOP gives Obama his revenue by letting tax rates rise for the rich (either those above $250,000 or those above $1 million) then what happens to tax reform (lowering of the rates, broadening of the base)? Perhaps this, too, gets thrown into the heap in the debt-ceiling talks. Then Republicans could claim they already gave the president his tax hike and now tax reform could be obtained in a revenue-neutral fashion.

The moving pieces here are many, and it is, of course, impossible to tell whether Obama has real interest in getting entitlement reform done. All of that said, so long as the GOP no longer feels obligated to do the impossible (keep all the Bush tax cuts) then multiple iterations become possible. Sometimes the best way to get what you want is to give up what you can’t have anyway.