Rep. Robert N. Giaimo (D-Conn.), chairman of the House Budget Committee, said he would rather see Congress give up its budget-control process than have it turned into a "charade" by the current conflict over defense and social spending.

"Either Congress is going to act like grown men and women," and reach a compromise on the 1981 fiscal year budget or admit to the public that it can't discipline itself on budget issues, he told a meeting of defense contractors yesterday.

There was no sign of substantial progress yesterday in the budget dispute, which finds the Senate backing an 1981 budget that increases military spending farther than the Democratic majority in the House will accept.

Until Congress approves a first budget resolution for 1981, no spending bills can be passed under the rules of the budget reform legislation passed six years ago. That deadline currently is holding up approval of nearly $15 billion in supplemental appropriations for 1980.

Giaimo said he is under tremendous pressure to put the budget process aside in the emergency and waive the rules, letting the 1980 spending measures be approved.

"I can't do it," he said. Such an end-run around the budget rules would be "the height off deceit."

One endangered program is a special unemployment benefit fund for 600,000 jobless Americans, which will go broke by Friday without an immediate infusion of money from Congress, the Labor Department said.

The department had expected the fund to run out of money yesterday, but officials said previously undetected surpluses have been found in agency bank accounts around the country.

"We will be totally out of money by Friday" although some states will run out before then, said a department official.

Affected by the fund cutoff are auto workers and others laid off because of foreign trade, former federal employees, ex-servicemen and former CETA public service job holders.

Giaimo blamed President Carter for throwing roadblocks into the budget-approval process by his last-minute opposition to the 1981 budget compromise reached by House and Senate negotiators late last month.

"If certain people in high positions had stayed out of the process, we'd be a lot closer" to agreement, he said. He stopped well short, however, of echoing the reaction of his counterpart, Sen. Ernest F. Hollings (D-S.C.), chairman of the Senate Budget Committee. Hollings called the president's opposition to the compromise attempt "outrageous, deplorable" conduct and political hypocrisy.

Yesterday, Giaimo and Hollings met with Carter to renew their case for a compromise. The White House had no comment on the outcome of the meeting.

Giaimo's current compromise proposal would shift $300 jillion in 1981 spending from defense to transportation and income security, while cutting $2 billion from the $171.3 billion budget authority for longer-range defense commitments.

"We're not that far apart," he said, "but we're hung up on symbolism."

Also on the budget front yesterday, Transportation Secretary Neil Goldschmidt told 10 big-city mayors during a close-circuit television conference call that "we don't have the money to fund" all the transit and urban highway programs that are both ffeasible and meritorious.

Several of the mayors expressed concern about what might happen to transit and highway grant programs in the budget conference. "How can I help?" asked Jake Godbold, mayor of Jacksonville, and his question was echoed by others.

The Carter administrtion had hoped to double appropriations for transit spending over the next decade as part of its response to the energy problem. Windfall profits tax revenues were to be earmarked for that program in the administration's proposal, but as Goldschmidt told the mayors, "the windfall profits tax is mostly going to the Defense Department." m