Bernanke said that a $60 billion cut along the lines being pursued by Republican in the House of Representatives would likely trim growth by around two-tenths of a percentage point in the first year and one-tenth in the next year.
"That would translate into a couple of hundred thousand jobs. So it's not trivial," he said in response to questions from members of the House Financial Services Committee.
The Republican-run House has passed a budget bill for the current fiscal year that includes $61 billion in spending cuts, but majority Democrats in the Senate say the reductions would endanger the economic recovery.
Any spending legislation must be approved by both chambers of Congress before it can become law.
Members of Congress are locked in a bitter fight over the budget, with Republicans, spurred on by Tea Party fiscal conservatives, having made deep spending cuts and immediate deficit reduction a top priority.
The Senate on Tuesday approved a House-passed bill to extend government funding for two more weeks, a move that averts an imminent shutdown of the federal government, but that does nothing to resolve the ongoing budget tussle.
The bill, which now goes to President Barack Obama for his signature, contains $4 billion in relatively noncontroversial cuts, a sum House Republicans see as just a downpayment on their larger goal.
Goldman Sachs economist Jan Hatzius estimated that the larger spending cut bill would trim 1.5 to 2 percentage points off of the annualized economic growth rate in the second and third quarters of this year.
Some of that pullback was already built into Goldman's GDP forecast for 4 percent annualized growth in the second quarter.
"Federal government spending enters directly into the Commerce Department's GDP estimates, so unless there is a full offset from other components of GDP a reduction in federal government spending must reduce GDP on impact," Hatzius wrote in a note to clients.