WASHINGTON — The fix for a faulty ignition switch linked to 13 traffic deaths would have cost just 57 cents, members of Congress said Tuesday as they demanded answers from General Motors’ new CEO on why the automaker took 10 years to recall cars with the defect.

At a hearing on Capitol Hill before a House subcommittee, GM’s Mary Barra acknowledged under often-testy questioning that the company took too long to act. She promised changes at GM that would prevent such a lapse from happening again.

“If there’s a safety issue, we’re going to make the right change and accept that,” said Barra, who became CEO in January and almost immediately found herself thrust into one of the biggest product safety crises Detroit has ever seen.

But as relatives of the crash victims looked on intently, she admitted that she didn’t know why it took years for the dangerous defect to be announced. And she deflected many questions about what went wrong, saying an internal investigation is under way.

Since February, GM has recalled 2.6 million cars — mostly Chevrolet Cobalts and Saturn Ions — because of the faulty switch, which can cause the engine to cut off in traffic, disabling the power steering, power brakes and air bags and making it difficult to control the vehicle. The automaker said new switches should be available starting April 7.

Barra was firm, calm and polite throughout the proceedings. But she struggled at times to answer lawmakers’ pointed questions, particularly about why GM used the switch when it knew the part didn’t meet its own specifications.

When she tried to draw a distinction between parts that didn’t meet specifications and those that were defective and dangerous, Rep. Joe Barton, R-Texas, shot back: “What you just answered is gobbledygook.”

She also announced that GM has hired Kenneth Feinberg — who handled the fund for the victims of 9/11, the Boston Marathon bombing and the BP oil spill — to explore ways to compensate victims of accidents in the GM cars. Barra stopped short of saying GM would establish such a fund.

Some of the questioners appeared surprised that Barra hadn’t reviewed the tens of thousands of pages of documents that GM submitted to the committee, and that she was unaware of some decision-making processes at the company.

Rep. Diana DeGette, D-Colo., held up a switch for one of the cars and said a small spring inside it failed to provide enough force, causing engines to turn off when they went over a bump.

DeGette showed how easy it was for a light set of car keys to move the ignition out of the “run” position.

GM has said that in 2005, company engineers proposed solutions to the switch problem, but the automaker concluded that none represented “an acceptable business case.”

“Documents provided by GM show that this unacceptable cost increase was only 57 cents,” DeGette said.

The 57 cents is just the cost of the replacement switch. The figure does not include the labor costs involved in installing the new part.

Barra testified that the fix to the switch, if undertaken in 2007, would have cost GM about $100 million, compared with “substantially” more now.

Under questioning, she said the automaker’s decision not to make the fix because of cost considerations was “disturbing” and unacceptable, and she assured members of Congress that that kind of thinking represents the old General Motors, and “that is not how GM does business” today.

“I think we in the past had more of a cost culture,” Barra said, adding that it is moving toward a more customer-focused culture.

Rep. Tim Murphy, R-Pa., chairman of the House Energy and Commerce Subcommittee on Oversight and Investigations, read from an e-mail exchange between GM employees and those at Delphi, which made the switch. One said that the Cobalt is “blowing up in their face in regards to the car turning off.”

Murphy asked why, if the problem was so big, GM didn’t replace all of them in cars already on the road.

“Clearly, there were a lot of things happening” at that time, Barra said.

In his prepared remarks, David Friedman, head of the National Highway Traffic Safety Administration, pointed the finger at GM, saying the automaker had information last decade that could have led to a recall, but shared it only last month.

Rep. Henry Waxman, D-Calif., said that House Energy and Commerce Committee staff members found 133 warranty claims filed with GM over 10 years detailing customer complaints of sudden engine stalling when they drove over a bump or brushed keys with their knees.

The claims were filed between June 2003 and June 2012.

Waxman said that because GM didn’t undertake a simple fix when it learned of the problem, “at least a dozen people have died in defective GM vehicles.”

Some current GM car owners and relatives of those who died in crashes were also in Washington seeking answers. The group attended the hearing after holding a news conference demanding action against GM and stiffer legislation.

Owners of the recalled cars can ask dealers for a loaner vehicle while waiting for the replacement part. Barra said GM has provided more than 13,000 loaners.