WASHINGTON — When President Barack Obama visits Ohio, a swing state heavily dependent on the auto industry, he said his bailout of U.S. car makers saved tens of thousands of jobs and argues that Republican presidential nominee Mitt Romney would have “let Detroit go bankrupt.”

Now that he’s heading to Nevada, the swing state hit hardest by the housing crisis, Obama on Saturday raised the memory of Romney’s similar statements on housing foreclosures.

“I know there are some who think that the only option for homeowners is to just stand by and hope that the market has hit bottom,” Obama said in his weekly radio address. “I don’t agree with that.”

Obama, who heads to suburban Las Vegas today, didn’t name Romney or quote him directly. But some might recall Romney’s interview with the Las Vegas Review-Journal’s editorial board in October 2011. Discussing the foreclosure crisis, he said, “Let it run its course and hit the bottom.”

His words stung many distressed homeowners in the state, and the Obama campaign hopes they haven’t forgiven Romney. But it’s now clear that Romney’s point wasn’t simply to let the market hit bottom.

Speaking in Las Vegas recently, Romney clearly had changed his tone, talking not about the “bottom” but about how to “reignite” the housing economy, get credit flowing again and spark housing sales.

Obama’s solution for continued recovery, reiterated in the radio address, is for Congress to pass his plan to cut red tape so responsible homeowners can save thousands on their mortgages by refinancing at today’s historically low interest rates.