The White House knows that if they cannot get the GOP to vote to increase rates, they will get crushed on the tax issue in the midterms. Their red state Democrats need political cover before they can vote to increase taxes. That cover is a Republican cave.
The White House also knows that if they can get the GOP to vote to increase taxes once, it will be far easier to get them to do it again.
Barack Obama needs the Republicans to raise rates. If they do not get it before January 1, all of the Bush tax cuts will expire and the GOP will not permit any reduction without it being an across the board reduction. Moderate Democrats in the Senate and the few remaining blue dogs in the House will be in a very difficult position.