[Update 1: Corrects year of SEC filing]

A Senate bill introduced Wednesday would place employees at Fannie Mae and Freddie Mac under a federal pay scale, similar to legislation already in the works in the House.

The new bill would also block any unpaid bonus payments at the mortgage giants, instead using them to pay down the national debt. The top executives received a combined $13 million in bonuses in 2010, according to the Securities and Exchange Commission.

Sen. Mark Begich, D-Alaska, and Sen. John Thune, R-S.D., introduced the bill, called the "Stop the Outrageous Pay at Fannie Mae and Freddie Mac Act."

"It is unbelievable that Congress needs to step in and end these outrageous salaries for Fannie Mae and Freddie Mac executives," Thune said in a news release. "The American taxpayers have already bailed out these agencies to the tune of over $150 billion and should not be on the hook for millions of dollars in exorbitant salaries."

Employees at the government-sponsored enterprises would earn a maximum of $275,000 annually under the federal pay scale, according to the Senate bill. Compensation would also be public without "compromising the privacy of individual employees," Begich's office said.

Executive pay at Fannie and Freddie has drawn repeated attacks from federal legislators, including during House and Senate committee hearings. A House bill, HR 1221, that puts the GSEs on a federal compensation level passed the House Financial Services Committee on a 52-4 vote in November.

The Congressional Budget Office estimates the House bill would reduce salaries at Fannie and Freddie by about $300 million each year. Still, the agency said the legislation "would have no significant impact on the federal budget" because the money saved would not go to the Treasury Department.

The two CEOs, Fannie's Michael Williams and Freddie's Charles "Ed" Haldeman, have said they will step down sometime this year. The Federal Housing Finance Agency, said last month it "anticipates a substantial decrease in CEO compensation" for the new chiefs.

Williams and Haldeman did not cite pay as a reason for leaving.