Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) joined congressional Democrats yesterday in shying away from cuts in Social Security cost-of-living increases as a means of reducing budget deficits.

"I'm not persuaded myself we should cut COLAs cost-of-living adjustments right now," Baker told reporters in what an aide later described as an acknowledgment of the difficulty of tampering with Social Security, especially in a congressional election year.

Baker's comments came as a surprise because congressional leaders and White House aides had been counting on some Social Security cost curtailment in working out a budget compromise that would keep deficits from soaring beyond $100 billion over the next few years.

One plan under consideration by the negotiators--a 4 percent cap on inflation adjustments coupled with a stretch-out so that future increases would come every 15 months instead of every 12--would save $12 billion next year and a total of $64 billion by 1985, according to the Senate Budget Committee.

But any cuts in Social Security have been a major sticking point for many Democrats, including House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), who has indicated reluctance to accept Social Security cuts, especially if President Reagan refuses to back off his tax cut program, which he did again yesterday.

In an apparent attempt to break this logjam, Baker said he doesn't think there should be a "quid pro quo . . . a trade-off" between taxes and Social Security and added that he believes O'Neill agrees.

Although some House Democrats are willing to talk about cuts in Social Security inflation adjustments, others, including House Democratic Campaign Chairman Tony Coelho (D-Calif.), are urging Democrats to hold firm on Social Security unless Reagan publicly urges cuts, which he has not done. "You don't play poker with one side laying down its hand and the other not even showing its cards," said Coelho. "That's naive." Democratic polls show that Social Security ranks second behind unemployment as a source of voter concern, Coelho noted.

For Democrats to take the lead in cutting one of their own programs to help Reagan reduce his budget deficits is to follow in the footsteps of British officers in "The Bridge on the River Kwai" who became so enamored with building the bridge that they forgot they were doing it for the enemy, commented a House Democratic leadership aide.

And yesterday Senate Minority Whip Alan Cranston (D-Calif.) said he flatly opposed any Social Security cuts "at this time."

In addition to political problems, Congress has been told that the deadline for computer reprogramming of Social Security benefits for fiscal 1983 is late next month. Moreover, prospects for big savings that might outweigh political disadvantages diminish as inflation subsides, as it has been doing in recent months.

The budget talks, which were suspended earlier this week, are scheduled to resume Sunday, with Democrats complaining that Reagan's reluctance to embrace proposed options remains an obstacle to compromise.

"The president's position has been one of a stranger and I regret it," said Sen. Ernest F. Hollings (D-S.C.), ranking Democrat on the Senate Budget Committee. "We are meeting in good faith," he said, in the talks with presidential aides. "The president is going to have to come on national TV and say we need it or it's not going to get off the ground."

O'Neill voiced a similar complaint on Wednesday, saying Democrats have extended Reagan "the hand of friendship, and he apparently does not want to seize it."

Sen. J. James Exon (D-Neb.), a Budget Committee member, also suggested Reagan will be responsible if the budget negotiations fail. "Unfortunately it's a game of political chicken with the only real loser being the American people and economy," he said, claiming Reagan is even "at odds" with his own Republican leadership in Congress.

Asked about Exon's assertion, Baker denied that Reagan is at odds with Republicans but conceded that "the Republican leadership is impatient." Baker, who plans to tell the Senate Budget Committee go start drafting a budget on its own if a compromise has not been reached by next Thursday, said he thinks there is a "discernible desire to work something out on all sides."