Norton said she would introduce a bill next week that would cut member pay starting in 2015, after the next Congress. That would comply with the 27th Amendment to the Constitution, which says legislative changes to congressional pay can only take effect after an intervening election.

But Norton also suggested a change to a 1985 law that was written in a way that prevents the current sequester from hitting member salaries. The Gramm-Rudman-Hollings Act of 1985 requires sequester cuts to apply to congressionally appropriated "accounts," or items listed in presidential budgets, but member salaries are not caught up by either of these classifications.

"The least Congress should do is update the 1985 law so that in the event of sequester cuts during any year in the future, members would share in the pain they are inflicting on the country and on federal employees," Norton said. "If we do not fix the 1985 law now, the American people will conclude that we have deliberately taken a pass on cuts to members' salaries."

Norton has said she would donate a day of her own pay for every day federal employees are furloughed because of the sequester. She said her donation would be directed to the non-profit Federal Employee Education & Assistance Fund, which offers loans and grants to federal workers in need.