Without a deal, the measures known as the "fiscal cliff" will take effect in January.
Bernanke also said Congress must raise the federal debt limit to prevent the government from defaulting on Treasury debt. Failure to do so would impose heavy costs on the economy, he said. Congress also needs to reduce the federal debt over the long run, he said, to ensure economic growth and stability.
Uncertainty about all these issues is likely holding back spending and investment and troubling investors, the Fed chairman said in a speech to the Economic Club of New York.
Resolving the fiscal crisis would prevent a sudden and severe shock to the economy, help reduce unemployment and strengthen growth, he said. That could make the new year "a very good one for the American economy," he said.
"A stronger economy will, in turn, reduce the deficit and contribute to achieving long-term fiscal sustainability," Bernanke told the group.
When asked during a question-and-answer session after the speech whether the Fed could soften the impact of the fiscal cliff, Bernanke was firm in his warning.
"In the worst-case scenario where the economy goes off the broad fiscal cliff . . . I don't think the Fed has the tools to offset that," Bernanke said.
The severity of the Great Recession, he said, may have reduced the U.S. economy's potential growth rate. He didn't say by how much or how long slower-than-normal growth might persist.
Over the long run, the U.S. economy has grown an average of about 2.5 percent each year. Bernanke said several factors have weighed on growth: Long-term unemployment has eroded many workers' skills and led some who have lost jobs to stop looking for one.
Companies have spent less on machinery, computers and other goods, reducing their production capacity. Stricter lending rules and uncertainty about the economy may have discouraged would-be entrepreneurs from starting more companies, the Fed chairman said.
By the end of December the federal government is expected to hit its borrowing limit.