President Reagan and House Speaker Thomas P. (Tip) O'Neill (D-Mass.) yesterday signaled strongly for the first time that negotiations aimed at reducing the 1983 budget deficit may succeed.

The key appeared to be acceptance by the president of some cuts in the large planned increases in defense spending and by congressional Democrats of a cap on automatic cost-of-living increases in benefit programs including Social Security. Some new revenue-raising measures, such as an oil import fee, may also be part of the compromise.

"I look forward to progress being made as soon as they Congress come back from the Easter recess," Reagan said at the White House. "That's why we are negotiating so fast."

On Capitol Hill, O'Neill said: "There's a possibility, there really is a possibility we could work something out. I don't think Reagan's as hardened on defense as he was." As far as he can determine, O'Neill added, the president is "still in cement" only on insisting that last year's business and personal income tax cuts not be reduced.

The signs of movement came as administration officials acknowledged the budget outlook has worsened as the economy has remained weak. Commerce Secretary Malcolm Baldrige said that because of a weaker-than-expected economy and other developments, it will take spending cuts of $20 billion to $30 billion on top of the $56 billion worth Reagan proposed in February to hold the 1983 deficit to $100 billion.

In other words, if no cuts are made and no taxes or other revenue-raising measures adopted, the 1983 deficit would be $175 billion to $185 billion. A final budget compromise--if it can be reached as a result of the delicate three-way negotiations among the White House, the Republican-controlled Senate and the Democratic-controlled House--likely would still leave the deficit in the neighborhood of $125 billion, observers said. But larger cuts could be made for later years so that the deficit could be steadily reduced if a sustained economic recovery is achieved.

Reagan again said he believes the economy is "bottoming out of a recession," but he added that unemployment--already at a post-World War II record of 9 percent--may continue to increase for a while.

Baldrige, at his breakfast meeting with reporters, acknowledged that some large corporations could go bankrupt this year. "My instincts tell me there will be one or two," he said, but he would not speculate on which industries or companies.

Murray L. Weidenbaum, chairman of the Council of Economic Advisers, also said the recession has hit bottom. "What we don't yet see are the signs of the upturn," he told the Washington Press Club. High interest rates are "the major sticking point," he said.

Neither the president nor O'Neill is participating in the direct negotiations among House and Senate leaders and presidential aide James A. Baker III. Four of the participants, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.), Senate Finance Committee Chairman Robert J. Dole (R-Kan.), House Ways and Means Chairman Dan Rostenkowski (D-Ill.), and House Budget Committee Chairman James R. Jones (D-Okla.), all said yesterday that they, too, are optimistic a compromise will be struck.

However, in Dallas at a meeting of the National Association of Broadcasters, they sounded a note of caution as well. "I'm optimistic. When you are negotiating, you have to be optimistic," Rostenkowski said. "The problem is that the principals are not in the room. The decisions will be made in the Oval Office and the speaker's office."

Reagan was asked whether there would be a "summit" meeting with House and Senate leaders on the budget. "I think that will be a part of the procedure before we finally arrive at a budget," he replied.

Domenici said a reduction in both cost-of-living increases for benefit programs and defense spending increases "will be part of a package." The budget chairman said "a little, tiny, stop-gap, interim holdup is in order" for the benefit increases and there will be less for the military."

Added Dole, "If we are going to have a package endorsed by both Democrats and Republicans, we are going to have to have defense cuts. That is the politics of it."

Reagan appeared to be indicating that he would accept some cutbacks in the big buildup in military spending he has planned. In response to a question about defense spending, he reiterated an earlier statement "that any government program obviously has areas where the savings can be made by management changes and so forth, and I am open to any suggestions of that kind." The president, however, also said he would oppose any cutbacks in his program to upgrade the nation's military weapons systems.

The president made no commitment to accept any particular budget change. "It so far has not reached a point in which it comes to me with any concrete proposals of one kind or another," he said.

But White House aides believe Reagan is, as one put it, "a shade more open to compromise" on defense issues than he is on any postponement of the tax reduction.

One likely casualty, if anything major is done in the area of weapons systems, could be the long-debated MX missile. Reagan is not enthusiastic about the missile, and spending for it has been held up by the Senate Armed Services Committee until the president decides exactly how it should be based, whether in hardened silos or on some kind of movable launcher.

Reagan was greeted by mixed boos and applause as he arrived to speak to a meeting of the AFL-CIO's Building and Construction Trades Department. The nearly 5,000 delegates cheered loudly when their leader, Robert Georgine, looked at Reagan and said, "I don't have to tell you how deep a recession the construction industry has slipped into."