The division you talk about is among political parties. Those independents/swing voters in my opinion do not feel the divide. Like every president before him, President Obama makes them happy at times and gets them peeved at him at other times depending on the issue at hand. The rift of which you speak of is not there for these independents which make up around 40% of the electorate. The rift is there between members of the parties, those who associate themselves with the two major parties. I agree to a certain extent that during his first two years in office, Obama didnít respect or give a hoot about the GOP. He didnít have to with the huge majorities he had in both chambers.
He got use to this and when 2010 happened, I think the president spent the next two years not know what to do. He needed to reach across to find a couple of Representatives or Senators from the opposing party that most presidents had done at the beginning of their first in the past. He is now trying to bring everyone together. Time will tell if he is successful or not.