THE WHITE HOUSE lets it be known that President Carter is reconsidering his promise to NATO last year to raise U.S. defense spending 3 percent. The reason is the current grave -- and totally justified -- concern with inflation. If the 3 percent increase were a purely domestic matter, or if it involved only a decision that the administration had made internally, this kind of reconsideration would be normal and desirable. But it was, in fact, a promise to this country's European allies, in return for which they were to make similar contributions in the common interest.

Mr. Carter's White House does not seem fully to perceive the damage that is done to his standing abroad by this kind of inconstancy. The issue here is not only dollars and guns, but political stamina as well. The European governments all readily recognize the nature of Mr. Carter's present embarrassment, since they themselves continually have to deal with their own versions of it. Voters no longer worry much about invasion from the East, and there's a constant temptation to divert money from defense to social benefits. But if the United States is not going to uphold its end of this bargain, it is idle to expect the Europeans to do any better. And if nobody is going to stick to the pledge, what is the point in continuing to have solemn summit meetings at which, with much fanfare, pledges continue to be made?

The debate over budget cuts, and who is to bear the burden of them, is going to be a far more savage and vehement one than simple arithmetic suggests. The budget deficit in this fiscal year, which began on Oct. 1, has been set at $39 billion. Mr. Carter has repeatedly said that the deficit next year, as an essential part of the campaign to reduce inflation, will be under$30 billion. But that will require cutting much more than $9 billion from current services. The nation's economic growth is slowing down, and a recession is probably not far ahead. Federal spending is likely to rise automatically -- because of unemployment compensation, for example -- and tax revenues are likely to fall below expectations. The present budget would swing into much heavier deficit. To keep the 1980 deficit under $30 billion will probably require cutting present services and spending levels something like $25 billion to $30 billion -- a dire reduction.

The awesome severity of this prospect is quite naturally bringing all sorts of commitments into question. But defense spending is the second subject within a month on which the administration has said that it is reconsidering an international pledge. In Europe last July, Mr. Carter promised to reinforce energy conservation in this country by letting the price of oil rise to world levels. Several weeks ago the administration said that it is thinking about retreating from that pledge.

The defense budget is not sacrosanct. Energy policy needs to be continuously readjusted to changing circumstances. Sometimes undertakings made in one climate have to be renegotiated in another. But the Carter administration seems to be falling into the habit of going to summit meetings, making agreements there, and then returning home to suggest that those agreements can be kept or not according to the exigencies of the moment. Asked about defense spending at his press conference yesterday, Mr. Carter replied that "I will be responsible," and that he will assess the defense program with great care. We have no doubt of it. The question is whether he will have an equal concern for this country's allies abroad, and their confidence in the stability of American intentions on the subject that matters most to them.