President Reagan acknowledged yesterday that he faces a tough fight on his proposed budget compromise as interest groups began mobilizing against it, led by senior citizens and Democratic members of Congress who accused him of breaking a promise not to reduce cost-of-living increases in Social Security benefits.

Speaking to reporters before leaving the White House for a 10-day vacation on his California ranch, Reagan said he was "very optimistic and hopeful" of getting the compromise, which would cut in half the increase in defense spending he had sought, and eliminate or curtail dozens of federal programs ranging from Amtrak to revenue sharing with local jurisdictions.

"It's going to be a fight. It's been a fight since 1981," Reagan said. "There are factions there that just want to keep on spending in Congress."

"This is going to be the most difficult imaginable proposition to win in the Senate, so we're going to worry about that right now and move on to the House later," Office of Management and Budget Director David A. Stockman said.

The original budget proposal Reagan submitted to Congress for fiscal 1986 is considered to be dead and a budget resolution worked out by the Senate Budget Committee was rejected by the president because it took too much out of defense and not enough out of domestic programs.

The compromise between the president and Senate Republicans announced Thursday would reduce Social Security costs by about $21 billion over the next three years and other retirement benefits by about $4 billion.

The reduction in the increase of the defense budget from the 6 percent after inflation that Reagan had sought to 3 percent after inflation would save an estimated $70 billion over the next three years.

Reagan denied that this would affect national security, as he contended when he submitted his original budget request in February.

"We didn't lower it to the point that had been suggested by some," he said. "Yes, it is a compromise. There are things that I think were worthwhile that will not be done now for a while and be delayed, but it will be a continuing increase and no weapons systems will be slowed down or cut out from the military budget, so that we can honestly say that with this our national security capability has not been reduced."

Many defenders of dozens of programs that the compromise would cut or eliminate were vowing yesterday to fight on Capitol Hill. But one of the principal battles is likely to focus on the proposal by the president and Senate Republicans to limit cost-of-living adjustments (COLAs) in Social Security and other federal retirement programs over the next three years.

Reagan said that if Democrats accuse him of breaking his word on this issue "they'll be lying in their teeth as they did in 1982" when they charged that he was trying to cut back on Social Security.

"They were talking about canceling the COLA ," he said. "We're approving a guaranteed -- more than 6 percent because it's compounded over a three-year period -- regardless of what inflation is."

Democrats in both chambers threw down the challenge yesterday.

Sen. Daniel Patrick Moynihan (D-N.Y.) announced that he would introduce an amendment when the budget reaches the floor to strip the Social Security provisions from it and restore the full COLA increases.

On the House side, Rep. Claude Pepper (D-Fla.), 84, a champion of senior citizens and chairman of the House Rules Committee, vowed to bring Social Security up for a separate vote on the House floor.

Reagan and the Democrats were engaged in something of a fight over semantics on the issue of Social Security COLAs.

Under the proposed compromise, they would be limited to 2 percent a year for the next three years if inflation is 4 percent a year or less. If inflation were to rise above 4 percent, say by 1 percentage point to 5 percent, recipients would get the 2 percent plus the 1 point over the 4 percent mark. Under law, Social Security recipients receive a COLA when inflation rises above 3 percent. Inflation is not expected to exceed 4 percent next year under current economic projections.

Reagan denied that this was a violation of his repeated promises in the 1980 and 1984 campaigns not to reduce Social Security benefits.

"How is adding a 2 percent raise each year cutting it?" he said.

Democrats and senior citizen activists, however, were circulating Reagan's statement to the American Association of Retired Persons (AARP) in October 1980:

"Any reform of the Social Security system must have one overriding goal: that the benefits of those now receiving, or looking forward to receiving, Social Security must be protected and that payments keep pace with the cost of living."

Pepper saw no room for argument on the issue.

"I'm shocked that the president of the United States would deliberately repudiate a solemn commitment he made to the senior citizens of this country that he would not cut Social Security benefits," he said.

Cyril Brickfield, AARP's executive director, said Reagan had "dishonored his pledge."

"Older Americans feel betrayed," he said at a news conference with Pepper. "Is it fair to give the Pentagon inflation plus 3 percent and at the same time ask older and disabled Americans to take inflation minus 2 percent?" he said.

A spokesman for the AFL-CIO said that the federation approved the proposed reduction in the increase in defense spending but strongly opposed the Social Security proposal.

"A 3 to 5 percent real increase in defense spending is what we called for," said spokesman Murray Seeger. "But we're dead opposed to using Social Security to bail out the president on his budget deficits by using money that's supposed to go to the elderly. The Social Security system is running a surplus, not contributing to the deficit, and having it in the general account disguises the size of the real budget deficit."

Other sticking points promise to be the termination of the Small Business Administration, Amtrak subsidies and general revenue sharing, among others.

The U.S. Conference of Mayors has called for a year's freeze on programs such as revenue sharing.

"The mayors have been strongly encouraged to meet with their congressional delegation in the next few days to let them know what the impact will be," said Michael Brown, a spokesman for the conference. He said elimination of revenue sharing after next year would force many cities to cut back on public safety programs such as police and fire protection and loss of urban development action grants would dry up about $4.3 billion in private investment that will create about 100,000 jobs.

A spokesman for Amtrak said the proposal to eliminate federal subsidies comes at a time when the corporation has completed a major capital investment program, steadily is cutting its operating deficits and moving toward breaking even. "We've rebuilt the Northeast corridor and have brand new equipment," he said. "Our on-time record is better than the airlines and we have increasingly attractive schedules. Our response is a Bronx cheer for it, but we'll wait and see what finally happens."

Senate Majority Leader Robert J. Dole (R-Kan.) has not decided how to proceed with the proposed compromise, according to his aides.

One option is to let the resolution reported out by the Budget Committee go to the Senate floor and offer the compromise as a substitute. Another is to ask the Budget Committee to pass a new resolution along the lines of the compromise.