Euphoria over President Carter's hard-hitting offensive against Ronald Reagan in the Cleveland debate possessed Carter's high command the instant the confrontaton ended, from abnormally ebullient Hamilton Jordan to effusively confident Stuart Eizenstat.

"We did it," Eizenstat told us. "We took the offensive, we held it to the end and we appealed to every constituency in the Democratic Party."

That euphoria by Carter insiders grown accustomed to the worst of political times for most of his presidency quickly shrank when Air Force One landed here in the cold light of Wednesday morning. Glimmerings of a sudden knockout blow disappeared, replaced by a hard truth: whatever else the debate proved, it left Carter's battle for reelection as unpredictable as before. That means Carter is striving even harder to nail Reagan not only as a nuclear arms races against the Soviet Union but also as a passivist willing to watch quietly as "terrorist" nations collect nuclear bombs of their own to threaten the world.

Emerging from Air Force One at the airport here, Al Barkan, who shared some of the presidental euphoria after viewing the struggle from a seat inside Cleveland's public music hall, got a dash of cold water from a top Pennsylvania labor strategist to meet the president.

"A standoff, Al," the union leader told Barkan. Barkan is chief of the AFL-CIO's political arm, COPE. He has played a key role in Carter's uphill struggle to overcome multiple economic disasters in his campaign. "A standoff, or at best the slightest tilt for Carter," Barkan was informed.

A somewhat similar disclaimer from the rampant optimism of Carter's top aides came from Ohio's popular Sen. John Glenn. Glenn warmly congratulated Carter at a post-debate victory celebration for scoring points against Reagan. Later, he remarked that in all his previous debates, Reagan had seemed to be defeated on points, but ended up winning.

Glenn's astute observation helps explain the Carterites' genuine post-debate glee. Television is as much a visual as an auditory medium, perhaps even more. Reagan's relaxed style, which has served him so well in previous political debates, may have carried more weight with the immense TV audience than Carter's tightly controlled self-discipline in holding the offensive. Although neither seemed unduly tense, Carter did reach for his glass of water 11 times in the 90-minute debate.

With hopes of a debate knockout dashed, and preponderant polling evidence giving Reagan an edge, the president quickly added a new line here to his war-and-peace attack on Reagan. Answering questions before a friendly audience at a town meeting in the Trinity Episcopal Cathedral in downtown Pittsburgh, he first set the stage with an unprovable claim that the panelists who asked questions at the debate believed that nuclear arms and the war-peace issue were their "preemient" concern.

He then charged that Reagan was taking an "extremely dangerous approach" to nuclear arms control by ignoring the risk of "radical or terrorist" nations' making nuclear weapons. Here was a fresh elaboration of Carter's favorite theme: that Reagan and nuclear arms are combustible. He singled out Iraq and Libya as just such "radical or terrorist" nations that must be denied the bomb (he did not say how). He tossed in Pakistan and South Africa, but not Israel, as other "dangerous" examples of nations that might acquire nuclear arms without impediments from President Reagan.

Intensification of that line of attack removes all doubts about the last few days of Carter's campaign from New York to California. His usually cautious aides indulged in overoptimism in assessing Carter's prowess in the debate, but that cannot obscure Carter's political mastery of submerging inflation, unemployment and high interest rates in the rhetoric of the campaign and elevating the war-and-peace issue. War, peace and nuclear arms are now all there is.

Considering that his voter approval rating in the polls one year ago was at record lows, Carter's success in forging that issue out of such meager raw material bespeaks political genius of a quality that transcends short-lived euphoria after the Cleveland debate.