"She essentially admitted fault within her office," Roberts said.
In a statement after the meeting, Napolitano said, "I pledge that the department has fixed the internal process that allowed this document to be released before it was ready."
It didn't take long for Napolitano to become a target for Republicans. In less than 100 days after she was confirmed secretary, two Republicans have called for her resignation.
At the heart of the GOP criticism is the right-wing extremism report.
When conservative bloggers began writing about the report, Napolitano defended the assessment while acknowledging that some of it should have been rewritten. She went on a number of television news shows to apologize and explain her support for and admiration of veterans.
A few Republicans took to the House floor this week to criticize Napolitano.
"Has this homeland security secretary gone absolutely stark raving mad?" Rep. Michele Bachmann, R-Minn, said Wednesday.
"I think the appropriate thing for her to do would be to step down," Rep. Michael Burgess, R-Texas, told Fox News on Thursday.
"Janet Napolitano should resign or be fired," Rep. John Carter, R-Texas, said on Wednesday.
Obama administration aides dismissed the criticism as a "typical Washington game" and "political theater."
Despite the furor among some Republicans, party leaders did not bring it up in a meeting with President Barack Obama and on Thursday. House Republican leader John Boehner had indicated it likely would be discussed Thursday. But his spokesman, Kevin Smith, said the topic was not broached.
White House spokesman Nick Shapiro said the right-wing extremist report originated in the Bush administration and Napolitano was working to keep the nation safe from terrorists.
"She doesn't have time for these games — and neither does the president," Shapiro said.
The veterans issue wasn't the only flap. Earlier this week, Napolitano drew criticism for flubbing an explanation of federal law prohibiting people without proper documents from crossing U.S. borders into the country.
In an interview with CNN, Napolitano, whose career has included stints as a U.S. attorney and attorney general and governor of Arizona, said: "Crossing the border is not a crime per se. It is civil."
While crossing the border illegally is a crime, most illegal immigrants caught in the United States face only civil penalties and deportation.
Sen. Jeff Sessions, R-Ala., characterized Napolitano's statements as one of the most "baffling" he has ever heard from a senior government official.
"It is breathtaking that a Cabinet secretary, bestowed by the public with the responsibility to protect our nation's borders, could be ignorant of the indisputable fact that it is a violation of the criminal code to enter our country illegally," Sessions said.
Napolitano spokesman Sean Smith said: "She may be new to Washington, but she has been around politics for a long time, and she knows political theater when she sees it."
Smith said Napolitano spent 16 years enforcing the law on the Southwest border. "Americans can rest assured that she understands what the law is along the border," he said.
She also has drawn criticism for claiming in an interview that the Sept. 11, 2001, terrorists entered the U.S. across the Canadian border. The Sept. 11 commission found that none came through Canada. But others have, such as the would-be millennium bomber Ahmed Ressam.
Discussing security along the U.S. border on Canada's CBC News on Monday, Napolitano said, "To the extent that terrorists have come into our country or suspected or known terrorists have entered our country across a border, it's been across the Canadian border. There are real issues there."
When asked whether she was talking about the 9/11 terrorists, Napolitano said: "Not just those, but others as well."
Smith on Thursday said Napolitano acknowledged she misspoke and had been thinking of the millennium bomber.