House Financial Services ranking member Spencer Bachus (R-Ala.) asked Bernanke whether offsetting an extension would require taxes to be raised or spending to be cut.
"The arithmetic is very clear. To get the deficit down, you have to have either more revenues, less spending, or both," Bernanke said.
The European debt crisis has put greater pressure on the U.S. government to look for ways to scale back spending and draw down deficits.
Bachus asked Bernanke if cutting spending would provide the confidence the economy needs to speed up recovery's pace.
"I think all options need to be on the table. We need to look at all the programs for their merits, both in terms of their short-term stimulative effects and also in terms of how well they would support growth in the long term," he said.
Lawmakers are weighing their options with some Democrats, including Senate Budget Committee Chairman Kent Conrad (D-N.D.), even saying now that tax cuts should be extended to help the economic recovery that has slowed down during the European debt crisis.
The Senate could begin action on the tax cuts before leaving for the August recess.