Federal Reserve Chairman Ben S. Bernanke called on lawmakers Monday to “take care of their job” and raise the nation’s debt ceiling, warning that default could derail the still-fragile economic recovery.

In a free-wheeling conversation at the University of Michigan’s Gerald R. Ford School of Public Policy, Bernanke said the debt limit has only “symbolic value” and advocated eliminating it. But he dismissed suggestions that the Fed’s policy of keeping interest rates low is taking pressure off Congress to act.

“We’re not going to be playing games with that. We’re going to follow our mandate,” Bernanke said. “Congress should take care of their job, which is to address the fiscal issues.”

Although he acknowledged that the rising national deficit is unsustainable over the long term, Bernanke said fiscal instability is holding back growth now. He estimated that tax increases and spending cuts in the recent compromise over the federal budget will reduce the nation’s economic output as much as one-and-a-half percentage points this year.

“The challenge is to achieve long-run sustainability without unduly hampering the recovery,” he said.

The 90-minute, unscripted talk was Bernanke’s first public appearance of the year and part of the Fed’s renewed efforts to engage the public and demystify the institution. Appearing relaxed before the audience of about 800 students and community members,Bernanke offered empathy for Main Street and a spirited defense of the Fed’s efforts to shore up the economy. The stubbornly high employment rate and the hardship it has caused for American households “motivates and justifies” the Fed’s aggressive measures, he said.

Bernanke cited rock-bottom mortgage rates that have fueled a rebound in the housing market and new construction jobs as evidence that its purchases of billions of dollars of mortgage-backed securities was paying off. But members of the Fed’s policy-making committee have begun to question how long the effort should continue and have expressed concern about the size of the Fed’s balance sheet.

“Broadly speaking, we have found this to be an effective tool,” Bernanke said. But, he added, “it is possible that as you move through time and a situation changes that the impact of these tools could vary.”

Even the location of the speech in hard-hit Michigan represented a departure for an institution often seen as insular.

“There are regional challenges, and coming to Michigan and the Midwest sends a different message in terms of public interest and engagement,” said Susan Collins, dean of the Ford School, who led the discussion.

Bernanke also fielded questions from audience members on topics ranging from the monetary policy’s role in creating asset bubbles to the feasibility of minting a trillion-dollar platinum coin to pay off the nation’s debt. (“I’m not going to give that any oxygen,” he said of the latter.)

The chairman even took a few questions from Twitter, turning the Fed into one of the top trending topics on the site.

“Was that 140 characters?” he quipped, after a question about whether the Fed was intentionally undershooting its 2 percent target rate of inflation.

Bernanke, a scholar of the Great Depression, also called upon the lessons of history in his talk. One of the greatest mistakes of central bankers in the 1930s was their fear of using unconventional tools to resuscitate the economy, he said. Few would accuse the current Fed of repeating that error.

“The Fed and other central banks did undertake some unorthodox policies,” he said. “Not all of them worked, but a lot of them did. We did help to stabilize the global financial system.”