Stan Collender thinks it's likely:
Back in September I said it was better than 50-50 that no deal would be in place by January 1. I raised that to 60 percent immediately after the election. Today, I'm raising my predicted likelihood of no deal before January 1 to 75 percent, and I may still be overstating the possibility that an agreement will be reached and put in place before the tax cuts and spending increases go into effect.
One reason why:
The fiscal cliff hits January 1 and Boehner's formal election as speaker is January 3. Any deal with the White House and especially a deal that includes the tax increases the White House wants, could cause Boehner to lose enough votes at least on the first ballot on January 3 to prevent him from being speaker. Even if he subsequently wins on a later ballot, he will be seriously weakened.