One idea circulating among at least a few Republicans would be for the House to pass one bill extending the Bush tax cuts for all but the highest bracket, and then another bill extending the Bush cuts for the highest bracket alone. Both would pass with Republican support, and both would go on to the Senate. There, majority Democrats would pass the bill for lower-bracket cuts with Republican support and would kill the bill for top-bracket cuts over Republican opposition. Voila — the tax rate for high earners would go up without GOP votes.

Some Republican lawmakers dismiss the proposal as “too cute.” And others are looking at other solutions. Since GOP opposition to a tax increase on the highest bracket is based in large part on the fact that many small businesses file as individuals and would be hit by a rate hike, some lawmakers are searching for a mechanism that would raise the rate on wealthy tax filers but not on top-bracket filers who have a certain number of employees.

The search for solutions doesn’t seem to matter to Obama, who has been reassuring allies on the Left that he’s not going to back down.