PRESIDENT REAGAN opened his defense of his next budget last night with his State of the Union address. He wants to hold spending next year at the same level, allowing for inflation, as this year. Since defense spending is rising rapidly, that would mean substantial reductions in everything else--reductions that Congress, including the Senate with its Republican majority, has already signaled that it will not accept.

His strategy to bring down the deficit includes the widely leaked idea of a standby tax--surcharges to go into effect only under certain conditions and, in any case, only after the next election. Congress has never accepted the idea of a conditional tax, and now the struggle will begin once again to drag Mr. Reagan, protesting, toward a realistic tax bill. Mr. Reagan is once again relying on Congress to rescue him from the ominous arithmetic of his own budget. Congress did it last year, extraordinarily well. Can Congress do it again?

Probably the most interesting sections of this address were those that dealt with education and job training. This is one area in which Mr. Reagan's sense of his responsibilities, and the government's, has expanded greatly since he took office. He's absolutely right in drawing attention to the need for more and better schooling in math and science for American children. Equally, he's right in emphasizing the urgent case for stronger public action in industrial retraining, and in the difficult process of getting young people securely established in their first jobs. These things will cost federal dollars, and they are worth them.

But you are entitled to doubt that Mr. Reagan will accomplish much for the quality of American schools by cranking up once more the campaign for a school prayer amendment. Similarly, it's disappointing to see the tuition tax credit make another appearance. Both the amendment and the tax credit are highly divisive, and threaten to do more than enough damage to counterbalance any good that may come from the president's more enlightened proposals.

Mr. Reagan touched only briefly on the pressing questions of international trade and the arms-control negotiations with the Soviets. Neither was a subject that could be fully addressed in a broad catalog like last night's address. But the references to both were welcome acknowledgment of their standing in the short list of the president's, and the country's, deepest concerns. On the arms negotiations he added the observation that "allied steadfastness remains a key to achieving arms reductions." That's a useful reminder to this country's friends in Europe and the Pacific that, as they must depend on us, so we also are depending on them. Perhaps it was an address characteristic of a president going into his third year, in the sense that the passages on international affairs were, on the whole, stronger than his prescriptions for policy at home.