Two powerful Republican Senate committee chairmen, Robert J. Dole (Kan.) and Pete V. Domenici (N.M.), predicted yesterday that the bipartisan Social Security rescue plan approved late Saturday by a presidential advisory commission will be approved by Congress, despite immediate opposition from groups representing businesses, government workers and the elderly.

"On the whole, I think it will work. I think it will pass. I think it will have broad support," said Domenici, chairman of the Budget Committee, on "Face the Nation" (CBS, WDVM).

Commission Chairman Alan Greenspan also said he expects passage, even though many parts of the plan are highly controversial.

"It's not going to be easy, but it's a terribly formidable group of political figures who are supporting this compromise," he said, referring to political leaders including President Reagan and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.). Greenspan spoke on "Newsmaker-Sunday" (Cable News Network).

Dole, the Finance Committee chairman, who played a key role in getting the agreement after dramatic, day-long talks that lasted into the night Saturday, said he is "very optimistic" that Congress can complete action on the plan by May 1.

The proposal will be considered first by the House Ways and Means Committee, which starts hearings Feb. 1.

If action is not finished by May 1, Dole said on "Meet the Press" (NBC, WRC), the Social Security Administration would have to start processing checks that include an annual cost-of-living adjustment (COLA) to be paid in July, even though the plan calls for postponing the increase for six months.

The plan, approved 12 to 3 by the commission, combines tax increases and curbs in benefit growth to net $169 billion over the next seven years and prevent default. But it contains some highly controversial provisions, such as taxing half of benefits to individual retirees with incomes above $20,000; accelerating scheduled Social Security payroll tax increases; mandatory coverage for new federal employes, and the six-month delay in the COLA.

Despite the broad political support, opposition to proposals for accelerating the payroll tax increases and imposing a federal income tax on Social Security benefits was voiced by the American Association of Retired Persons.

"We understand the spirit of the compromise, but it has yielded a package that has some very fatal flaws," said Laurie Fiori, a legislative aide to the AARP. "We think public sentiment is going to be very negative."

The American Postal Workers Union attacked a provision requiring federal workers to join Social Security, as did many other federal employe unions.

The National Federation of Independent Businesses, an association of small businesses, said it opposes the plan because proposed payroll tax increases would add to the tax burden on businesses and aggravate unemployment.

The AARP said it has begun forming a coalition to oppose the plan. According to several sources, other major groups preparing to oppose it include the U.S. Industry Council and the U.S. Chamber of Commerce.

Sen. William L. Armstrong (R-Colo.), one of the commission members who voted against the proposal, said he plans to introduce legislation to raise the retirement age.

"The question is how strongly outside groups will weigh in," Armstrong said. "If they weigh in powerfully, then we've got a horse race and a chance to make significant improvement. If they don't, then I think it is a relatively small number of members of Congress who are going to fight that battle . . . ."

Several members, including Domenici, noted that the commission recommendations did not include specific proposals to cover the last one-third of the long-term Social Security deficit. Even some who backed the report also favor raising the retirement age.

Although some business groups were lining up in opposition, the two leading business spokesmen on the panel, Alexander Trowbridge, president of the National Association of Manufacturers, and Robert Beck, president of Prudential Insurance, agreed to the plan.

Negotiations Saturday were emotionally charged by the approaching midnight deadline for the commission report and by the tension of political bartering at the highest level, between the president and the Democratic leadership.

Three times, White House representatives to the commission--chief of staff James A. Baker III, congressional liaison Kenneth Duberstein, budget director David A. Stockman and presidential assistant Richard G. Darman--walked across Pennsylvania Avenue to Blair House, where the commission was meeting, and three times they walked back. Each time, Baker said only: "We're still working."

The agreement was completed by early afternoon, according to three commission members involved in the negotiations, but the White House and Democratic leaders could not agree on a statement announcing the deal. About six hours later, at 9 p.m., it was agreed that there would be separate statements.

The commission was created in the fall of 1981 after Reagan proposed a Social Security plan assailed by members of both parties. The president withdrew the plan but, in the recent election campaigns, Democrats charged him with seeking massive cuts in Social Security benefits. Polls showed that the issue was crucial to helping Democrats pick up 26 House seats in last year's elections.

Although the commission had held meetings for a year, it appeared moribund in November, unable to reach agreement between Democratic demands for solving the problem mainly through new taxes and Republican demands for a solution based mainly on curbing benefits.

Reagan, fearful of making himself vulnerable to further political attack, hesitated to advance proposals for cuts but continued to oppose tax increases.

On Jan. 3, when the commission had only two more weeks of life, Sen. Daniel Patrick Moynihan (D-N.Y.) tapped Dole on the shoulder at the Senate session opening the 98th Congress and, according to Dole, asked:

"Are we going to let this commission die without giving it one more try?"

Dole, sensing Democrat readiness for a compromise, invited Moynihan and Democrat Robert M. Ball, the skillful and knowledgeable former Social Security commissioner, to meet with him. The three agreed to invite Greenspan and Rep. Barber B. Conable Jr. (N.Y.), senior Republican on the Ways and Means Committee, to join them the next day.

Greenspan, in turn, revealed that he had been discussing the possibility of a compromise with White House staff members, including Baker and counselor Edwin Meese III. Baker, Stockman, Darman and Duberstein became the White House negotiating team and worked out the final compromise with the Dole-Moynihan group.

The key problem was molding a compromise that combined benefits cuts with tax increases, and the agreement had to be sold simultaneously to Reagan and O'Neill and endorsed publicly at the same time, a delicate arrangement.

Ball became the Democrats' chief negotiator, according to Dole and Conable, and with Greenspan devised the proposal to tax Social Security benefits. Ball and Moynihan were in constant touch with O'Neill and other Democratic members of the commission: AFL-CIO President Lane Kirkland, former representative Martha Keys (Kan.) and Rep. Claude Pepper (Fla.).

For some Democrats, the decision to seek a compromise was fueled by fear they would be seen by the public as blocking a compromise for political reasons.

Other Democrats wanted to avoid heightening public fears that the system could not be fixed.

White House willingness to compromise was sparked by fear that Democrats would use the issue to continue attacking the president as a foe of Social Security. He has repeatedly denied that charge.

Another White House motive was a desire to be able to factor into the forthcoming 1984 budget any reductions in net spending for Social Security and lower the federal deficit.

The final compromise came when negotiators agreed to balance $40 billion in COLA cuts against $40 billion in accelerated tax revenues and when the White House negotiators told Reagan that taxing benefits could be seen essentially as a benefit reduction rather than a tax increase.

Adjustments in the accelerated tax schedule and in offsetting the extra payments against income tax won the support of several conservative members of the commission.

Although Pepper was not a member of the inner negotiating group, the fact that he has become chairman of the House Rules Committee this year was used as a bludgeon by Ball and Moynihan to force Republicans to drop some of their benefit cuts.

They argued that Pepper, 82, the most vocal supporter of maintaining all benefits for the elderly, would block a floor vote on the bill.

When the final agreement was reached Saturday, Reagan issued a carefully worded statement that revealed his political anxiety about the agreement. He edited the announcement himself before it was released to the press and, at the top, placed O'Neill's name ahead of his own.