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WASHINGTON — The recovery of the American auto industry, which repaid a significant part of its debt to the federal government on Tuesday, has sparked a political battle over who deserves credit and who deserves blame.

On the day that Chrysler wrote a check repaying $5.1 billion to theUnited States Treasury, President Obama and his Democratic allies claimed credit for saving a crucial industry in Michigan, a state that will be a critical battleground in the 2012 presidential election.

“Supporting the American auto industry required making some tough decisions,” Mr. Obama said in a statement, “but I was not willing to walk away from the workers at Chrysler and the communities that rely on this iconic American company.”

Democrats also sought to highlight past statements from Mr. Obama’s likely Republican rivals, who had criticized the president for a federal bailout that they said was unnecessary and wasteful.

The Democratic National Committee on Tuesday released a YouTube video highlighting a 2008 opinion article by Mitt Romney in The New York Times titled “Let Detroit Go Bankrupt.” In the video, Mr. Romney, a former governor of Massachusetts, is shown asserting, “If you write a check, they are going to go out of business.”

In 2009, Mr. Romney said Mr. Obama’s plans for rescuing the automobile industry were “tragic” and “a very sad circumstance for this country.”

A Romney spokesman said on Tuesday that the president’s plan was modeled after one Mr. Romney advocated in 2008.

“Mitt Romney had the idea first,” said Eric Fehrnstrom, a Romney spokesman, citing the Times opinion article. “You have to acknowledge that. He was advocating for a course of action that eventually the Obama administration adopted.”