The Republican-controlled Senate yesterday voted 65 to 34 to scuttle a proposed cutback in Social Security cost-of-living adjustments as it began dismantling a deficit-reduction plan drafted by President Reagan and Senate GOP leaders that it endorsed in principle only the day before.

Defying warnings that the action would "set the stage for an unraveling of the whole package," the Senate bowed to political pressures and agreed to retain full cost-of-living increases for Social Security recipients.

But yesterday's vote, even though it was expected, amounted to a serious setback for the GOP budget plan to cut spending by $300 billion over the next three years in order to halve the government's $200 billion annual deficits.

In a measure of the enormous political sensitivity of the Social Security issue, 19 Republicans, including 11 of the 22 up for reelection next year, joined all Democrats except Sen. John C. Stennis (D-Miss.) in voting against the proposed cutback.

The vote jeopardized $34 billion in proposed savings from all government pension programs, more than one-tenth of the deficit reductions anticipated for the next three fiscal years under the entire plan.

It also created an edgy climate for consideration today of the budget plan's proposal to limit defense spending increases to 3 percent above inflation, or half what the Reagan administration wanted. Pressure is strong to cut it even further, perhaps allowing an increase only to cover the costs of inflation, which sources said would reduce the likelihood of Reagan's support for the entire package.

In an all-out administration push for the 3 percent increase, Defense Secretary Caspar W. Weinberger was lobbying personally for it off the Senate floor yesterday, and Reagan is expected to phone wavering senators today from Bonn, where he is attending a seven-nation economic summit.

Sources indicated that the 3 percent increase faced defeat last night if it were put to an immediate vote. The vote was put off until today.

Although Senate leaders conceded that a series of votes to pick apart the package was likely, Majority Leader Robert J. Dole (R- Kan.) predicted that a compromise with substantial deficit reductions, including savings from Social Security, eventually will be passed.

"We'll try to keep it the package together as best we can," Dole said. "A week from now we'll put it back together, like Humpty Dumpty," he added, overlooking the fact that the nursery rhyme character who fell off a wall never got reassembled.

Dole suggested a Social Security compromise might take the form of a one-year benefit freeze, as proposed earlier by the Senate Budget Committee and recommended by some Democrats but rejected by Reagan in favor of the proposal voted on yesterday.

The Reagan-backed proposal would have cut inflation adjustments by roughly half over the nel Patrick Moynihan (D-N.Y.) charged that Reagan created a "deliberately contrived deficit crisis" to shrink government programs and now seeks to "blame it on the recipients of social insurance."

Although Democrats had been spearheading the drive to kill the Social Security cutback, the proposal that passed was a Republican one -- proposed by Dole to assure that it bore the names of Sens. Paula Hawkins (R-Fla.) and Alfonse M. D'Amato (R-N.Y.) as chief sponsors. Hawkins and D'Amato had won this as the price of their support for the overall package on the initial procedural vote on Tuesday.

"If we had truth in labeling in the Senate, it would bear a Democratic label," Assistant Minority Leader Alan Cranston (D-Calif.) complained. "This amendment constitutes a move by a number of Republicans to repudiate President Reagan on the issue of Social Security," he said.

Republican leaders defended the Social Security proposal as an effort to get a handle on big entitlement programs and to spread the burden of deficit reductions to everyone.

"You can't put a reasonable package together without asking everyone to sacrifice a little," said Sen. Pete V. Domenici (R-N.M.), noting that 500 programs are affected in some way by the cuts.

Moreover, Sen. William L. Armstrong (R-Colo.) said, the amendment to kill the Social Security cut was "a killer amendment . . . a wrecker amendment . . . that sets the stage for an unraveling of the whole package."