How do you define "moving to the center?" From the #analysis of most of the conservative world, HW Bush, Dole, McCain and Romney lost because they were too centrist, and W Bush only won reelection because he was "lucky" enough to be Prez when 9/11 happened. As far as Obama goes...
Obama did not support same-sex marriage in 2008 (he only supported civil unions).
Obama never championed (or spoke about) a $15/hr minimum wage, or even a $12/hr minimum wage
Obama kept combat forces in Afghanistan
Obama chose the compromise, Republican-conceived path to universal health coverage
Obama avoided talking about race relations at all until forced to by current events
Obama was a free-trader actively involved in negotiating the TPP.
Obama's immigration policies were partially responsible for net migration of undocumented immigrants back to Mexico in his second term.
If Barack Obama had been pro-life, he might have done well as a Republican.
It is true that Obama was further left than any President since LBJ, but that's because Clinton was a pure centrist, and you could argue Carter was center-right.
Carter has been the most sympathetic towards the likes of Cuba, Venezuela, and Palestine of any President in recent history, and even during his presidency was probably the most dovish of the post-war era. He pardoned all draft dodgers. He engaged in almost no violent conflicts (outside the failed Operation Eagle Claw). He sought peace agreements at every turn. He opposed the death penalty. He was also miles ahead of his contemporaries on issues like Civil Rights and energy/the environment. He ultimately voted for Bernie Sanders, for Christ's sake! Just because he deregulated the airlines and the beer industry, that doesn't make him "center-right." I would argue he was and is actually more left than Clinton, who himself is not "center-right" despite what some people claim.
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