WHENEVER reporters and pollsters ask the right question, they get an answer from Americans that tells us clearly why Ronald Reagan's presidency has stayed up where others definitely would have sunk: People everywhere join in hoping that this administration can be rehabilitated. People generally think Reagan showed himself to be a terribly inattentive leader, or worse, in the dealings with Iran. But even at his lowest ebb - just before his speech to the nation on TV that eased his problem - his approval rating had only dropped to 42 percent.
That's low for Reagan. But considering the ratings of Carter, Nixon, and Johnson when they fell upon bad days, it is remarkable that Reagan could get such high grades just as his own commission had announced that it had probed Irangate thoroughly and found the President sadly lacking.
Then, immediately after a speech in which the President said he had, indeed, messed up badly and that he had learned his lesson, and that he would try to do better, a New York Times-CBS poll showed his performance rating shooting up to 52 percent.
Now that is a public show of confidence in a man whose presidency had been pretty much written off by the press and by politicians of both parties. But it also reflected this warmth that the public has long held for this President. This widespread affection for Reagan doubtless made it easier for the public to forgive. Nixon and Johnson would never have been let off so easy - nor would Carter, for that matter.
People are finally growing tired of seeing their government badly impaired in administration after administration. This doesn't mean they are becoming any less impatient with ineffectiveness or corruption. No, they want that sort of thing dug out and destroyed.
But Americans are coming to realize that they are the losers when an administration becomes disabled. They therefore are beginning to see the need to salvage a presidency if at all possible: Not simply because they love the man, as many people do Mr. Reagan - but because they want a president who can get the job done. Kenneth Adelman, director of the US Arms Control and Disarmament Agency, was trying to convince reporters the other morning that the intense presidential interest now in a Soviet arms-control proposal stemmed entirely from the fact that Gorbachev had agreed to Reagan's proposal, made at the Iceland summit. Mr. Adelman would not concede that Reagan was moving hard toward an arms pact in order to build up his standing with the public in the wake of the Iran debacle.
Moreover, Adelman said there was little in recent history to show that presidents benefited much in public favor after negotiating arms pacts - and he cited Carter and Ford as examples of presidents who gained little in the polls from achieving such pacts.
But Reagan and his people know full well that an arms-reduction treaty would do much to silence his critics, reestablish his clout with Congress, and bolster his performance ratings.
An arms pact would give the President the kind of lift that other chief executives whose administrations have faltered have been denied. It would be a dramatic achievement that would reinstate him in the public's eye as a leader. He could then be highly effective to the end.
All this is not to predict that Reagan will be able to do what has been impossible before - to reconstruct a presidency that seemed to have fallen apart. But his TV speech and press conference took him far in that direction. And, his appointments of Howard Baker, Frank Carlucci, and William Webster were also strengthening moves that showed Reagan at his astute best.
``Now, finally,'' writes columnist David S. Broder, ``the break has come, and no one should minimize the extent of the changes that have been made. The President and his reputation remain at risk so long as the investigations continue and so long as large questions - involving the diversion of money into still unknown hands - remain unanswered. But meantime, what is in effect the third Reagan administration has begun.''
Reagan can put his presidency together again - because the public would like to see him do it.
Godfrey Sperling Jr. is the Monitor's senior Washington columnist.