President Reagan, confronting several political brush fires, said last night that he is sympathetic to the "very real problem" of debt-squeezed farmers, that tax reform will mean lower taxes for all but those corporations paying little or no taxes now, and that budget director David A. Stockman is sorry for criticizing farmers.

Reagan used the nationally televised news conference to try to cool these domestic policy hot spots, all of which have flared up since his inauguration a month ago.

He opened the news conference with a statement celebrating "the strongest performance in a single year by the American economy since 1951." He vowed to "prolong and protect this expansion," and said tax-reform legislation "can and should be passed this year."

He issued a renewed appeal for his spending cuts to bring down the budget deficit but warned that he would stand firm against a tax increase. "That issue was debated and decided on Nov. 6," he said. "We intend to proceed with the mandate that we've been given by the people."

The president was questioned about Stockman, who stirred a furor Feb. 5 when he told the Senate Budget Committee that "I can't figure out why the taxpayers should have the responsibility to go in and refinance bad debt willingly incurred by consenting adults who went out and bought farm land when prices were going up and thought they could get rich."

Reagan said Stockman "has apologized for some of his remarks," saying Stockman's outburst was a response to "a certain amount of harassment and heckling" from Congress. "I could understand a fellow blowing his cool," Reagan said.

Stockman has not publicly apologized for his remarks about farmers, but has expressed regret for criticism of military pensions.

Only last week, Stockman said some farmers will be forced out of business in a "fundamental shake-out" because they overinvested in earlier years. Reagan last night offered sympathy to the farmers from the budget director and himself.

"I think he feels, as we all do, and I certainly feel myself, yes, the farmers have a very real problem and a lot of it has to do with policies that led to the runaway double-digit inflation that we had in which their land became a haven for those who were seeking hedges against inflation. All of these, plus the government programs, have left them with a very problem. And we're going to do our utmost to help them find a solution to it."

The president said Stockman would remain in the administration. He defended the administration's proposed cuts in farm subsidies and insisted that its debt-restructuring would "meet this present crisis."

"We won't pull the rug out from under anyone instantly who has geared themselves to these government programs . . . . I think you'll find that a great majority of farmers believe that the answer to their problems is out in the free market. And then if government is to help, then we should help by opening up world markets for them, by holding trade negotiations because much of the farming elsewhere in the world is government subsidized. And we intend to do all that we can."

On this and other topics, Reagan appeared to be parrying more troublesome domestic problems last night than he faced at his last televised news conference Jan. 9.

Reagan had stirred questions about his commitment to a Treasury Department tax-reform proposal when he seemed reluctant -- in a Feb. 7 interview with The Wall Street Journal -- to embrace a shift in tax burdens from individuals to corporations, as the Treasury plan envisions by eliminating many existing tax breaks.

Last night, Reagan said he had misunderstood the question. "What we're talking about, as to more revenue from business, is from those elements of business that have not been paying taxes," he said.

Reagan said it wasn't from businesses that are cheating but just "the way some of the exemptions had worked out." He went on to suggest "we want to change that so there will be a reduction in rates for everyone." This has been a politically appealing goal for Reagan throughout his presidency.

While rates may be reduced, Reagan did not acknowledge, as does the Treasury plan, that corporations will in effect pay more in taxes because they lose many existing breaks. This increase helps keep the plan "revenue neutral," which means it will not increase or decrease existing revenues.

On another politically charged subject, Reagan was asked about reports that he intends to allow the so-called voluntary restraints on Japanese auto exports to expire next month. Without directly confirming this, Reagan said discussions are going forward with the Japanese with a goal of "the two of us as trading partners having fair trade and free trade between us.