Barber noted that the sequester forced the Department of Homeland Security (DHS) to announce furloughs for thousands of border agents, which he said amounts to a 40 percent cut in pay.

DHS has said it would delay those furloughs to examine what flexibilities it has to mitigate the impact of the sequester, although furloughs are still expected.

Barber's bill, the Pay Cut for Congress Act, would take a 20 percent bit out of members' salaries, more than cuts in the range of 5 to 8 percent that other members have proposed.

Member pay was not explicitly cut by the sequester, but lawmaker salaries are exempt because of the way the sequester was written. The cuts, called for by the 2011 Budget Control Act, follow the rules of sequestration set out in a 1985 budget law.

That law requires cuts to programs that Congress specifically appropriates or that can be found in presidential budgets — but member salaries do not appear in either, and so they are spared.

In contrast, the salary of the President is explicitly exempt from sequester by the 1985 law.

The pay of the President's cabinet members are also exempt from sequester because their pay is technically seen as tied to the office they hold, not how long they work each day or each week. Nonetheless, some Obama administration cabinet members have said they would donate some of their pay to charity in light of the sequester.

President Obama himself has said he would donate 5 percent of his salary to charity.