Both candidates did their followers proud. But neither had good answers to hard questions. So the Great Debate points up anew the crisis of American politics. It defines the gap between a self-indulgent public opinion and the harsh realties confronting the country.

Gov. Reagan entered the debate at the edge of a cliff. He has a slender information base. He is prone to loose statement. There is in the country at large a widespread impression of a big-time meanie subject to the kind of itches that end up as war and hard times.

In the debate, Reagan walked skillfully around those hazards. He made no mistakes of consequence. He showed himself as an agreeable fellow with a nice sense of humor. He had a good word for peace, and for the aged, and for people trapped in central cities.

At one point he even came on strong with numbers. He laid to rest -- once and for all, I hope -- the president's spurious claim that his administration began the restoration of national defense after eight years of Republican cuts.

Carter needed a lift from the debate -- to be born yet again. His stretch drive to mobilize the Democratic constituencies has slowed in the last week. The latest inflation numbers focus attention on an inglorious chapter of his administration. So does the rush of attention to the hostages in Iran.

In the debate, Carter scored undoubted points. He controlled the dialogue and consistently put Reagan on the defensive. Most important, instead of sounding like a computer, he presented his arguments on two critical subjects in board, historic terms understandable to all Americans. First, Carter showed that, like all past presidents, but unlike Reagan, he favored arms control in an unmistaken and unambiguous way. Second he showed that, unlike Reagan, he stood in the "mainstream" of his party in supporting programs that promote health, education and job opportunities for ordinary Americans. On a strict man-to-man basis, Carter, in my view, came out slightly ahead in the debate.

But the biggest winners by far were the journalists who put the questions, or rather the questions themselves. For neither candidate showed the glimmerings of a capacity to cope with the national problems, to master the difficulties facing the nation, to govern effectively.

Dealing with foreign adversaries -- mainly the Soviet Union but also the radical Third World countries prone to practice blackmail and terror -- represents the most important problem. Especially since it affects oil supplies. Arms control is Carter's answer.

But he cannot get the SALT II treaty with the Russians past the Senate. He ham-handed efforts to limit the spread of nuclear weapons have been counterproductive -- witness the supply of material and equipment to Iraq by France, Italy and Brazil. Moreover, while important in itself, limiting the flow of nuclear arms is a distant and remote approach. It is indeed a moralistic cop-out on the messy, daily problems of living with the Castros and ayatollahs and Qaddafis of the world.

A similar cop-out, however, comes from Reagan. He wants a generalized increase in defense spending. But that will neither bring the Russians to terms nor count much in distant places like the Persian Gulf. It is a mark of flabbiness that Reagan answered Barbara Walters' question on Iran by coming out for a congressional inquiry. It is sheer witlessness for him not to point out that while Carter cannot pass a SALT treaty he, Reagan, can.

Inflation presents another critical problem. Reagan proposes a tax cut bound to be highly inflationary. Carter favors a tax cut that is only slightly less so. Neither gets at the root of the problem -- wage and price increases. Indeed, both swear off the subject.

A third crucial question -- though nobody had the courage to pronounce the word -- centered on the problem of race. Both candidates talked vaguely of progress. But neither faced up to the undoubted fact that helping minorities requires more spending by the federal government.

The refusal to face these facts, the preference for the moralistic cop-out, is not peculiar to Ronald Reagan and Jimmy Carter. It is the national condition, the state of opinion in the country. That is why we have Carter and Reagan as candidates this year. It is way, for the next four years, we can expect very little in the way of public achievement.