The Senate, marching in virtual lock step with President Reagan on budget priorities, emphatically rejected a proposal yesterday to scale back the automatic cost-of-living increases for Social Security and other federal benefits.

The proposal, by Sen. Ernest F. Hollings (D-S.C.), would have saved $2.6 billion in fiscal 1982 by pegging cost-of-living increases to a wage index if it rises less than the Consumer Price Index. The increases are based on the CPI, and many argue that it overstates the effect of inflation on living costs, especially for retirees.

Hollings' proposal was defeated, 86 to 12, with nearly all Democrats and most Republicans refusing to go along with tampering with Social Security benefits, especially in light of Reagan administration opposition to any changes in the cost-of-living index at this time.

To no avail, Hollings argued that Reagan's budget-cutting efforts would fail without some clampdown on indexed programs.

"We'll send him over to the hospital a present and tell him the country is turning around," said Hollings. "That's bunk. We're sending it faster than we're receiving it. Why? Because of this provision."

Despite their unbroken losing streak so far on the budget, Senate Democrats yesterday continued to pound away at Reagan's proposed spending cuts for social programs in the apparent hope that history will prove them right.

But even many Democrats appeared to be tiring of the effort by their more liberal colleagues to get a recorded vote on every politically sensitive budget cut. As the hours grew longer, the vote margins appeared to be growing wider.

One exception was a proposal from Sen. Dennis DeConcini (D-Ariz.) to cut "waste, fraud and abuse" within government by $1.7 billion. Over objections from Hollings, ranking Democrat on the Senate Budget Committee, that it was a symbolic gesture that would "break down the credibility of the whole [budget] procedure," most Democrats flocked to support it. But it lost, 53 to 43.

After five days of debate on $36.4 billion worth of spending reductions for the next fiscal year, passage by the Senate of the first phase of the Reagan program was a forgone conclusion. The only question was when.

As of mid-afternoon, Democrats were still walking around with about 20 amendments, most of them aimed at restoring funds for social programs Reagan has proposed to cut back or eliminate.

Republicans, confident of eventual victory, let the Democrats talk on, nudging them occasionally in hopes of finishing the day's end.

Meanwhile, the GOP majority, aided by conservative defectors from the Democratic ranks, easily beat back amendments to restore money for energy conservation and solar energy development, health services, youth job training and a variety of other domestic programs.

Most of the proposals lost by margins of roughly 2 to 1.

In the most comprehensive proposal of the day, Sen. Bill Bradley (D-N.J.) pushed unsuccessfully to restore $295 million for mass transit, Conrail, scientific research and job retraining in the fiscal 1982 budget. It was defeated, 76 to 22, with Bradley failing to get even a majority of the Democrats to go along with him.

A proposal by Sen. Howard W. Metzenbaum (D-Ohio) to restore $300 million for youth job training fared only slightly better, losing by a vote of 74 to 24.

Sen. Edward M. Kennedy (D-Mass.) scored a little better as he lost, 62 to 36, in an effort to put back $125 million for preventative health and community health programs.