President Reagan last night endorsed the "concept" of a constitutional amendment requiring a balanced budget as "the answer to uncontrollable government spending," but he avoided embracing the proposal awaiting action in the Senate.

Reagan said he still is looking at the amendment sent to the floor by the Senate Judiciary Committee, which would require a three-fifths vote of both houses of Congress to spend more money than the government takes in. He said he would prefer to see a provision added to put some limit on taxes "so that in the future you just couldn't always have a balanced budget by simply sending the bill to the taxpayers for whatever the deficit might be."

Actually, the proposed amendment, which some administration aides and outside economists oppose as too restrictive, already has a tax limiting provision.

The president's careful endorsement of a constitutional amendment came at his news conference last night in response to one of several questions on the recession, the large budget deficit he has recommended for next year and the frequently heard assertion that his economic program is tilted toward the rich and against those most in need.

As he has done several times recently, Reagan said he is willing to work with Congress to break the budget impasse, rejecting any notion that he is deaf to opposition to his proposals, much of it coming from his own party.

"I am listening, and I'm not inflexible and remaining a great stone face," he said, noting that his chief of staff James A. Baker III has been holding budget discussions with members of Congress for the last two weeks.

He said he could live with "management improvements that will result in great savings" in defense spending as long as such cuts did not retard efforts to "rebuild our defenses in view of the Soviet superiority."

But he indicated less willingness to accept changes in his program of personal tax cuts, saying, "You don't increase taxes in a recession."

The president demonstrated a certain touchiness about what he described as the "fairy tale, the myth" that his budget cuts have fallen heaviest on the poor who have no political clout.

He said that he had increased spending for college student loans, the elderly poor and the blind above the level spent during the Carter administration and that a substantially greater portion of his budget is going to programs benefiting individuals than in the Kennedy years.

The president, who has been stung by criticism of cuts he is proposing in social programs, noted also that total spending would rise by $32 billion. Critics say most of the increases are for his military buildup.

Reagan expressed personal concern about the 8.8 percent unemployment rate and the rise in business bankruptcies, now at a 40-year high, but ruled out short-term government programs to deal with these problems, saying "artificial stimulants" in previous recessions caused inflation to skyrocket.

Confidently, the president said that he believed the recession is bottoming out and that "we are safe in saying there is going to be an upturn in the second half of the year."

He acknowledged that high interest rates are blocking economic recovery but said they remain high because financial markets do not believe that "we will stay the course, bring down government spending and hold inflation down."

"There is nothing that government can do about this except hope that we can prove to them that we are serious about continuing this program," he said.

However, economists inside and outside the government have said they believe interest rates remain high because the markets believe Reagan's future budget deficits will be higher than Reagan has estimated. They also cite a belief by investors that the stalemate between Reagan and Congress over the fiscal 1983 budget will lead inevitably to even higher deficits.