President Carter promised yesterday to send Congress a budget with "severe cutbacks" in spending next year and "to take the political heat" from any groups that oppose reduced federal spending as part of the effort to restrain inflation.

Describing inflation as "the worst domestic problems we have," Carter said he met with Cabinet officials yesterday morning and told them to expect the 1980 fiscal year budget he will send to Congress in January to be "very tight."

The president cited no specific figures, but it is known that he has already ordered a slash in spending that would reduce the fiscal 1980 federal dificit to $37.5 billion - more that $13 billion below the $50.8 billion deficit now projected for fiscal 1979.

"I am perfectly willing to meet any special interest group, no matter how benevolent, and hold my own in spite of the political consequences," the president told a nationally televised news conference here.

Moreover, he added, the effort to restrain inflation may extend beyond fiscal 1980, which begins Oct. 1 next year.

The comments were among Carter's strongest on the subject of inflation, clearly identifying the struggle to hold down wages and prices as his chief domestic target and most severe political problem.

Carter conceded that inflation would grow worse, predicting it could reach 7 percent this year. But once again he rejected any resort to wage and price controls, something he has done consistently for more that a year, in an attempt to ease the fears of businessmen who oppose controls.

"We are doing everything we can to hold down the rate of inflation short of wage and price controls, which I never intend to impose short of national calamity," he said.

The president said fighting inflation is difficult without a "spirit of common sacrifice." Groups such as business, labor unions, teachers and farmers, while they may have worthy reasons for increased federal support, must understand that "this year at least, perhaps next year as well, we have got to restrain inflation," he said.

"I'm willing to take the political heat to do it," he added.

Carter's comments on inflation came in response to a question that noted the recent suggestion of former Federal Reserve Board chariman Arthur Burns that the president voluntarily take a $20,000 a year pay cut as a symbolic gesture in the fight against inflation.

Carter cited the freeze he has imposed on pay raises for federal government executives and the fact that Congress is considering a similar freeze for itself and federal judges.

As for Burns' suggestion, he said, "I don't remember Dr. Burns volunteering to take a pay cut" when he was in government.

Carter's remarks came as, separately, several of the nation's major banks announced another quarter-percentage-point rise in the prime rate - the interest they charge their most creditworthy corporate customers - in part a response to concern about inflation. (Story, Page D1)

Led by Continental Illinois Bank of Chicago, the banks raised their prime rates to 8 1/2 percent, up from 8 1/4 percent. It was the second increase in the prime rate in a month, and followed an upward push on interest rates by the Federal Reserve Board.

In another development, Robert S.Strauss, the president's chief anti-inflation advisor, expressed surprise yesterday at the refusal of U.S. Steel Corp. to hold price increases this year to below 1977's increases, saying the administration would oppose such action as inflationary.

In a speech in Dallas, Tex., Strauss said he was "somewhat surprised" that U.S. Steel Chairman Edgar Speer "did not see fit to contact me" about the company's pricing plans. Strauss said any price increase in excess of last year's increases would be "counterproductive" and inflationary.

Meanwhile, top Carter administration officials have begun exploring the possibility of trimming several billion dollars in spending from the fiscal 1979 budget the White House submitted last January, partly as an added anti-inflation move.

In addition to setting a tight spending target for fiscal 1930, as reported several days ago, policymakers are hoping to propose spending cuts of between $2 billion and $5 billion for the coming year's budget, which takes effect Oct.1.

The move would be designed first as an anti-inflation gesture, to help persuade the Federal Reserve Board to stop raising interest rates, and second to make it easier for the administration to reduce the budget deficit in fiscal 1980.

A $2 billion to $5 billion spending cut would bring the fiscal 1979 deficit below $50 billion, which officials consider a psychological benchmark.

However, officials cautioned yesterday that, in part for technical reasons, any cutbacks for fiscal 1979 would be difficult to make. Congress just recently set spending targets for the year aiming at a $50.8 billion deficti, and is well along in the appropriations process.

Administration officials still have no firm proposals onwhere to cut spending iin the fiscal 1979 budget. However, insiders day defense, because of its size, would be one primary target. The rest of the cuts would be made piecemeal throughout the budget. A decision is expected early in June.

President Carter already has made one major anti-inflation gesture by trimming $5 billion from the $25 billion met tax cut he proposed last January. Officials said the spending reductions now being considered would come on top of that change.

Meanwhile, Federal Reserve Board Chairman G. William Miller told the Senate Banking Committee yesterday there was "not much" the Fed could do to stem the rise in interest rates as long as inflation continued at its present pace. But he promised an easing if prices slowed.

In response to committee members' questions, Miller indicated the Fed still hoped to maintain economic growth at a pace rapid enough to keep the unemployment rate stable or declining, but he confirmed that output probably would rise somewhat more slowly "than we thought last year."

He also urged banks to become more "conservative" in their lending practices, to avoid any danger of over-extending their capital. Miller said the nation's banking system still is in "good" health, despite the recent rise in loan demand - "not very good and not excellent, but good."

The moves by the administration represent an important shift in over-all economic policy. In the past few weeks, the White House has altered course from a policy designed to combat unemployment to a plan aimed at battling inflation.