Barely three months after President Reagan pledged never to tamper with the Social Security system, the politically sensitive program has become a prime target of key GOP lawmakers and others in the effort to find a formula for reducing the massive federal budget deficits.

Led by Senate Majority Leader Robert J. Dole (R-Kan.), Republican senators have steered the budget debate carefully toward this inevitable collision between political and economic priorities, despite bitter memories on both sides of similar fights during Reagan's first term.

The growing likelihood that an effort will be made to delay or limit cost-of-living increases in Social Security benefits as part of an overall budget freeze sets the stage for a major struggle this year that not only would pit Republicans against Democrats but also could enlarge fissures in both parties over difficult fiscal issues.

The fight also could produce strange bedfellows. Reagan has ruled out a freeze on Social Security cost-of-living increases in his new budget, and an aide to one House Democrat said, "There's great sentiment among Democrats in helping President Reagan keep his promise."

The president's opposition hasn't deterred GOP senators. Dole, who said Friday that Republicans will write their own budget in the Senate, began hinting at the need to rein in Social Security almost from the day he was elected majority leader in mid-December. Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) and newly elected Majority Whip Alan K. Simpson (R-Wyo.) have supported him.

Last week, Dole organized a well-publicized hearing in which former chief economic advisers to three presidents told the Senate Finance Committee that significant progress on reducing the deficit could not occur without touching Social Security.

Dole's motivation in raising such a politically delicate issue is not clear. Some members of Congress say they believe he may be doing it to force Reagan to accept larger defense cuts.

"I assume that is the motivation," Sen. Daniel Patrick Moynihan (D-N.Y.) said. Others say they believe Dole is paving the way for Reagan to accept such cuts as part of an overall budget compromise.

Dole's effort puts him on a collision course not only with the president but with his counterpart in the House, Minority Leader Robert H. Michel (R-Ill.).

"It sounds to me as if they're going to pursue that course," Michael S. Johnson, Michel's press secretary, said of developments in the Senate. "But we are not."

Johnson called reductions in Social Security "off the table" because, in Reagan's first term, Republican candidates "got beat over the head" when the White House tried to cut benefits in 1981.

Reagan's aborted attempt to cut the program eventually led to a political truce and a bipartisan commission that assembled a package of tax increases and future benefit cuts to keep the system from going bankrupt. Republicans reluctantly bought the higher taxes and Democrats swallowed hard on the benefit cuts. Once approved by the commission, the package moved quickly through Congress in the spring of 1983.

The talk about Social Security cuts is all the more extraordinary because of the issue's role in the presidential campaign last fall. In the first presidential debate, Walter F. Mondale goaded Reagan into saying he would not go after the program after the election.

"A president should never say never," Reagan said in Louisville, "but I am going to violate the rule and say 'never.' I will never reduce Social Security benefits to people that are now getting them."

But when Mondale later accused the president of having a "secret plan" to cut Social Security, Reagan went further. "The president will never stand for a reduction of Social Security benefits for anybody," said White House spokesman Larry Speakes. White House officials said there would be "no tampering" with the system, in the form of either reduced benefits or higher taxes, except for those in the pipeline from the 1982 rescue package.

That put the issue to rest in the campaign, but it resurfaced quickly after Reagan's landslide victory.

Limiting the Social Security cost-of-living adjustment (COLA) has gained acceptance as part of an overall freeze on federal spending -- the direction Senate Republicans appear to be heading. Republican governors, meeting in Des Moines in December, told Vice President Bush they favored a spending freeze that included defense and federal entitlement programs like Social Security.

Even some Democrats find the idea attractive. "The nice thing about this is fairness," said Rep. James R. Jones (D-Okla.), who chaired the House Budget Committee during Reagan's first term and earlier proposed limits on the Social Security COLA. "I think the public, including recipients of [entitlement] programs, are willing to sacrifice if it is perceived as fair-share sacrifice."

Rep. William H. Gray III (D-Pa.), newly elected chairman of the Budget Committee, said Friday that the House should try to cut the deficit without touching Social Security, but he left the door open. Saying he was "hopeful" of putting together a budget resolution that did not affect Social Security, Gray added, "We may not be able to do that."

Freezing the Social Security COLA for one year would produce a net budget savings of about $6 billion in fiscal 1986, rising to $8 billion in fiscal 1988. That looks like easy money to lawmakers stymied over how to make major reductions in the deficit, especially with Reagan resisting large cuts in the Pentagon budget. But opponents say these politicians have their eye on the wrong target.

"They are not causing the deficit, they are reducing the deficit," Moynihan argued, saying that Social Security trust funds now show a surplus.

On that score, Moynihan agrees with Reagan, who said in the campaign that Social Security "has nothing to do with balancing a budget or erasing or lowering the deficit."

The keys to an eventual compromise may be Reagan and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), whose bitter fight over the issue in 1981 led to the bipartisan commission. So far, O'Neill is waiting for Reagan and the Republicans to show their hand. "The speaker said he will respond when the Republicans present their program to the American people," spokesman Christopher J. Matthews said.

But another leadership aide warned that Democrats would skewer Republicans on the issue. "Democrats very likely would make that an issue against our Republican brethren," he said. "The atmosphere is very poisoned from the last campaign."

The other question is whether Reagan can find a way to wiggle out of his campaign promise. Democrats already anticipate that happening. Said Jones, "I'm always amazed at his ability to unlock himself."