As a centrist, Obama's policies are not the cause of the polarization we see today, it is more the result of many factors in the media and political landscape. To the extent that Obama himself is polarizing it has more to do with his name, race, and views expressed while campaigning for his first term, not his actions or policies as president. Most significant is the growth of influence of the right wing media outlets, Fox news in particular, but various web sites are also significant. It has resulted in a large number of people who not only have their own views, they have their own facts.
Reagan was the most polarizing president since Nixon because he and his cohorts didn't just implement new policies, they attacked a large portion of the country culturally by stepping up censorship of erotica, passing more extreme drug laws, fighting unions, and verbally and politically attacking people who rely on government benefits, liberals, artists, academics, the counter culture etc. Not only that, they disregarded, circumvented and broke the law to implement their policies when Congress and the courts tried to rein him in, esp. with Central America (arms to Iran, secret funding of the Contra's terrorist activities, support of death squads and dictators, cocaine smuggling etc).
Bush II may have been more like Reagan with the culture wars, they were planning to do it (remember the large number of firings of US Attorneys in 2001?), if the post-9/11 events and wars didn't keep his administration so occupied. Those events distracted the public and provided apparent justification for some of their policies, but it took a long time for the mainstream media and public to realize what was happening. Because of fear of post-9/11 accusations of being soft on terrorism, the mainstream media and Democrats in Congress and Senate went along with many of the Bush II administration's policies, so it was difficult for them to criticize them until the negative consequences became too obvious for the public to ignore. The result was that Bush II was very polarizing to well informed urban dwellers (the left), but it wasn't until the end of his administration that the polarization was at a high level with the mainstream.