Congress and President Obama have 7-9 weeks to work out a deal prior to the expiration of the Bush tax cuts. When these tax cuts end, almost all the paycheck earners in America will have some nasty news, hence there is HUGE incentive for both parties to strike a deal. (For those who need a review: The GOP wants to keep all the tax cuts. The Dems want to end the tax cuts for the highest earners.)
Obama has issued a veto threat, but he won't have to veto anything. The Senate won't be passing anything the prez can't sign. Boehner is pretending he won't budge, but he surely will due to the huge incentive I mentioned above. There is also the recent history, which includes Dems and GOP negotiating the August 2011 debt deal and the GOP caving on the Social Security tax cut extension.
So there will be a deal, either before the end of the year or early in January. It might be a deal to extend the tax cuts a few months as serious negotiations take place, but there will be something. The exact form of the deal I can't predict. However, I definitely predict that Dems will include sunset provisions or other provisions that don't take effect yet, but require additional votes. This will provide Dems with leverage that is so valuable. The Dems will also try to reduce GOP leverage by including automatic debt ceiling increases without a vote.
I predict some very disappointed Republicans/conservatives. This is an easy prediction because the Dems have a lot of leverage, and the GOP is in a very weak position.
Elections have consequences
By the way, the sequester issue is not nearly as major because Obama has a fair amount of control over the timetable for parceling out the sequester cuts. He can make them tougher or gentler as he needs for his negotiating position. He's already announced that they will start off gentle, especially on defense contractors. Again, this is a leverage advantage for the Dems.
Update 11/17/12. There are so many angles on this, that I forgot a few that I wanted to mention. The deal will come out of the Senate, and the House will reluctantly pass amid much gnashing of teeth and perhaps some vomiting. In this way, the House will continue its tradition of NO COMPROMISE, that is, passing dozens of grandstanding bills before caving to the deals worked by some senators. Sigh. I'm tired of these children--maybe we should abolish the House.