This, from the Pew Research Center, should give you some idea:
In short, when asked whether Obama was doing enough to work with Republican leaders, 34 percent of independents said he was doing too little, compared to 13 percent of Democrats. Only 29 percent of independents said that he was doing enough to work with the GOP. If you're hoping for Obama to spend the next year railing against Republicans, you should prepare to be disappointed; as long as independents believe Obama hasn't done enough to work with the GOP, he will continue to make overtures in their direction, whether it makes sense or not.
-- Jamelle Bouie