“I remember well one time when I was very little and I was fighting with my brother every other minute, and my mother put us in a back room and said, ‘Don’t come out until you got it figured out,’ ” Mrs. Murray said. “We stared at each other for a while, but we came out friends.”

Panel members resent invasions of their privacy. “We like to eat breakfast without having cameras in our face,” Representative Jeb Hensarling, Republican of Texas and co-chairman of the panel, told reporters last month.

The panel, officially known as the Joint Select Committee on Deficit Reduction, has been dubbed the super committee by many because it has extraordinary authority to recommend changes in any spending or tax laws, and its recommendations cannot be amended before the House and the Senate vote on them this year.

Senator Dean Heller, Republican of Nevada, said it should be called the “super-secret committee.”

“We are opposed to inside baseball,” he said. “That’s what we are seeing in this super committee.”

Senator Mike Lee, Republican of Utah, said: “I understand the argument that the secrecy will facilitate robust discussion. But the American people have come to expect openness and transparency in the legislative process. I am not aware of any situation where a legislative committee responsible for matters of such profound sweeping importance operates in secret.”

Some panel members have met with lobbyists for groups trying to protect the benefits, contracts and tax breaks they receive from the government. Advocacy groups like the Sunlight Foundation and the Brennan Center for Justice have urged the panel to disclose such meetings, saying voters have a right to know who is lobbying for special treatment. And they want panel members to disclose campaign contributions within 48 hours of receipt.

“The secretive activities of this committee fly in the face of all the promises of transparency by Republicans and Democrats over the last few years,” said Brian H. Darling, a fellow at the conservative Heritage Foundation.