With opposition mounting to any deficit-reduction package that includes even modest cuts in Social Security, congressional and White House budget negotiators yesterday scrambled to find other sources of the roughly $2.6 billion in savings they need to reach their goal.

But the search proved inconclusive, and some participants in the talks said yesterday that an agreement may not be reached by Friday when, under the revised balanced budget law, across-the-board spending cuts of $23 billion automatically go into effect. That deadline could be postponed by congressional action.

At yesterday's daylong session -- the 16th in the talks, which have now entered their fourth week -- much of the momentum that appeared to be growing last Friday disappeared. Some negotiators had indicated on Friday that an agreement on a $30 billion deficit package was near.

Over the weekend, whatever collective will there was for a three-month delay in paying cost-of-living allowances to federal workers and retirees, including Social Security recipients, seemed to melt as quickly as last week's snow. The delay in the cost-of-living (COLA) payments would have saved about $2.6 billion, and was a key to achieving about $5 billion of reductions in entitlement program outlays. That $5 billion was the linchpin of an overall $30 billion deficit reduction that included about $10 billion in higher taxes.

Rep. Pat Williams (D-Mont.) attributed the loss of resolve to a combination of assessments by congressional leaders that any package with COLA reductions would fail and opposition by organizations that lobby on behalf of the elderly.

"In politics, perception is reality," said Williams, "and the perception given on the Sunday talk shows was that both the House and Senate would be reluctant to accept restraint on COLAs. Once that perception was given, it became reality."

The proposal to delay the inflation-driven COLAs for three months lost further steam yesterday morning, when a broad coalition of labor unions and elderly advocacy groups flexed political muscle at a Capitol news conference.

"There will be political fallout if this is pursued," threatened Arthur S. Flemming, former secretary of the old Department of Health, Education and Welfare. Groups that weighed in against the COLAs proposal ranged from the American Association of Retired Persons to the American Federation of Government Employes.

Rep. Claude Pepper, the 87-year-old Florida Democrat who chairs the House Rules Committee and serves as a powerful protector of the elderly, said in a videotape that if a deficit-reduction agreement between Congress and the Reagan administration includes reductions in Social Security COLAs, he would insist on a separate vote on that provision on the House floor.

One of the negotiators, Sen. J. Bennett Johnston (D-La.), said the COLA issue was not entirely dead but was certainly ailing.

The alternatives to the $2.6 billion in savings the COLA changes offered were politically unacceptable to many Democrats. They included such areas as health and welfare programs for the needy.

The new setback in the talks appeared to leave both sides weary and frustrated. "I feel like a repairman at Chernobyl," said Williams, in reference to last year's Soviet nuclear accident.

Meanwhile, President Reagan yesterday threatened to veto housing legislation under Senate consideration, calling it a "budget-buster."

"This bill could add as much as $7 billion more in spending than I requested for this year," he said.