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Obama leads 53 percent to 39 in Michigan, down only slightly from the same poll conducted in February, when the president held a 16 percent lead.

Romney’s father, George Romney, was once governor of Michigan, and Romney spent his childhood there. Still, the poll found that most — 65 percent — don’t consider Romney to be a Michigander.

Romney’s favorability rating in the Wolverine State is deep underwater, with only 35 percent of those polled having a favorable view of him, compared to 67 unfavorable. Obama is at 53 favorable and 41 unfavorable in the state.

Romney’s stance on the auto bailout is hurting him among voters in Michigan. Fifty-five percent said Obama’s policies toward the auto industry are superior, compared to 31 percent who said Romney’s are better.

Democrats have argued that Detroit automakers would have gone belly-up without the $80 billion in federal loans they received.

In 2008, Romney famously penned an op-ed in The Wall Street Journal titled "Let Detroit Go Bankrupt." The Romney campaign has taken to arguing that the president adopted Romney’s idea for a managed bankruptcy, although many believe that there were no private investors around during the financial crisis who would have stepped in to provide loans had the government failed to do so.

While Michigan has swung reliably Democratic in recent presidential elections, Romney struggled to win his home state during the Republican primary in late February, at one point trailing in the polls to then-upstart Rick Santorum.

Romney won the state by 3 percent, but effectively split the delegate count with Santorum. Many called it a blown opportunity for the former Pennsylvania senator, who got wrapped up in controversial social issues just prior to the primary.

Michigan is one of 12 key swing states that will be critical in determining the outcome of the 2012 election.