Congressional supporters of the Renegotiation Board scrambled yesterday to set up one last effort to save the small watchdog agency before its operating funds run out on March 31.

Sen William Proxire (D-Wis.) and 12 cosponsors proposed legislation -- to be offered as a floor amendment to the Senate's pending business, the debt ceiling bill -- that would extend the life of the board through 1981.

Proxmire said yesterday that he had no idea whether his amendment could pass, but that he considered the elventh-hour effort worth a try because "we-ve got nothing to lose."

The board, a 27-year-old agency that recoups "excessive" profits from firms that sell defense and space material to the government, will be terminated at the end of the month unless Congress acts by then to extend it.

Even if Proxire's amendment, which may reach the Senate floor Monday, is approved, his effort faces uncertain prospects at best in the House, which seems more hostile to the board than the Senate.

At a House Banking subcommittee hearing yesterday, witnesses and most subcommittee members agreed that the board is as good as dead.

Subcommittee Chariman Joseph Minish (D-N.J.) read a letter he received Wednesday from the White House expressing the Carter administration's support for continuing the agency.

But the first witness, Rep. Paul McCloskey (R-Calif.), one of the leaders of the drive to kill the agency, expressed skepticism about the White House pledge.

The hearing also dealt with the government's authority to control defense profits if the board is terminated. ,under a quirk in the law, the board's demise will automatically implement a more rigid profit-control mechanism, the Vinson-Trammel Act, which prohibits profits over 10 percent on contracts for warships or their parts and 12 percent on airplanes or their parts.

Defense contractors, who lobbied hard to kill the Renegotiation Board, are at least equally disturbed about the prospect of complying with Vinson-Trammel.

"That law's goint to have to be amended at least," said Charles W. Stewart, president of the Machinery and Allied Products Institute, a contractor group. "Everybody's waiting for the next shoe to drop."

The Internal Revenue Service has said it will start enforcing Vinson-Trammel on April 15. But Stewart said yesterday that most industry groups expec3 the deadline to be extended pending congressional action.