He portrayed the scandal as part of a larger problem with the safety culture at GM, saying the automaker's training materials discouraged employees from using words like "defect" or "dangerous" when reporting trouble up the chain of command.
"The fact that GM took so long to report this defect says there was something very wrong with the company's values," Friedman said.
GM received a $49.5 billion bailout from Washington during its 2009 bankruptcy, and the government was once the automaker's majority shareholder, but it sold off the last of its GM stock in December.
GM stock closed Friday down just 36 cents, or 1 percent, at $34.
GM is already making changes. It has named a new safety chief and has begun checking records for problems that could lead to recalls. So far this year the automaker has issued 24 recalls totaling 11.2 million cars and trucks.
"We have learned a great deal from this recall. We will now focus on the goal of becoming an industry leader in safety," Barra said.
Earlier this year, after a four-year criminal investigation, the Justice Department made Toyota pay $1.2 billion for concealing unintended acceleration problems from NHTSA. No individuals were charged with a crime.
While the maximum fine that the Transportation Department can impose was doubled to $35 million this year, Foxx urged Congress on Friday to raise it to $300 million.
Even though GM's bankruptcy shields it from some past liability, the company has hired lawyer and compensation expert Kenneth Feinberg to negotiate settlements.
Carl Tobias, a law professor at the University of Richmond, said the government's action Friday "makes GM's exposure to liability greater, or the damages for which families ultimately settle larger."
Under the agreement, GM has to give NHTSA full access to the results of an internal investigation being done for the company by a former federal prosecutor. It will probably be finished in about two weeks.
Auto Writer Dee-Ann Durbin contributed. She and Krisher reported from Detroit.