INFLATION will be cured, according to President Reagan, by cutting federal spending to balance the budget. Unless, of course, inflation pushes spending up faster than the administration can cut. There was a wealth of instruction, not to say warning, in the little incident this week in which the White House disclosed an understatement of $3 billion to $6 billion in next year's spending estimates. That means another $3 billion to $6 billion to be cut from next year's budget, to stay within even the rather high figure that the president has set for the deficit.

One leading reason for the underestimate is evidently the very rapid rise in hospital bills, pushing up the cost of Medicare and its hospital insurance for people over 64. Medicare is one of Mr. Reagan's untouchable seven, the "social safety net" programs that are to be exempt from budget cuts and constraints. The president does not believe in reducing these benefits. Neither does he believe in trying to control hospital costs by legilation. Consequently, the rising patient costs are being multiplied against the rising numbers of elderly people in the American population. The cost of Medicare rose 14 percent from last year to this year alone. The Carter administration expected it to go up another 17 percent next year -- and that's the figure that is, evidentaly, too low. Last year the Health and Human Services Department was trying to maintain a guideline holding the increase in hospital costs to 13.5 percent. As it turned out, hospital costs actually rose 16.5 percent. The reasons have little to do with the familiar triology of waste, fraud and abuse. It's much harder than that. It's a demand to which this society has no good answer. The amounts of money that can be spent on medical care, particularly for elderly people, particularly for the treatment of serious and chronic ailments, are literally unlimited. Providing this kind of care is a proper and humane purpose to which to devote public funds on a large scale. But it is difficult to defend spending, even for the best of purposes, that increases without limit.

The Reagan administration doesn't defend it. The administration merely refuses to deal with it. Mr. Carter had tried to set a limit, in a gingerly way. It was beaten down by the hospital lobby. Now his successor is finding that even the Carter budget, with its wry acknowledgment of defeat on this point, has underestimated the prospect for Medicare next year.

Reagan has reacted by telling his staff to cut other spending to make room for Medicare. But that process can't be carried very far without infringing equally urgent claims on the federal dollar. Mr. Reagan exempted Social Security and Medicare from his budget reforms because he does not wish to frighten retired people, or endanger his high standing among them. But sooner or later he is going to have to recognize that federal spending on health care is on an accelerating curve that, unrestrained, will jeopardize else that he is trying to accomplish.