The story around Washington goes like this: "Do you think Carter is a one-term president?" The answer given after a pause, presumably for solemn deliberation: "Yes, I think he'll just make it."

That is attributed to the cynical maverick former senator Eugene McCarthy. In 1968, McCarthy's running for the presidential nomination had a lot to do with getting President Lyndon Johnson to bow out, although Johnson could have run for a second full term.

As a boom of sorts develops for Sen. Edward M. Kennedy, the other side of the dump-Carter movement, the question being widely debated is whether the president can be denied renomination by his party for a second term. Kennedy consistently keeps saying that he is for Carter's renomination and reelection.

But, while they will not talk about it publicly, what is happening in Iowa has sent a current of excitement through Kennedy's bustling, overcrowded office on Capitol Hill. The same movers and shakers who gave Carter his head start when he began to run two years before the election are now calling for Carter's replacement by the senator from Massachusetts.

A key figure is Charles Gifford, director of community action for the United Auto Workers in Iowa (with 65,000 members). Gifford and other trade unionists, who gave the Carter candidacy its big push four years ago, are saying today the nation needs more forceful leadership -- which Kennedy can provide.

The Gallup poll shows Carter's approval rating lower at midterm than any of his five predecessors in office at a comparable period. In the February poll Carter stood at 43 percent approval, 41 percent disapproval and 16 percent don't-know. Richard Nixon in his first term stood at 56-33-11.

While poll ratings fluctuate with yo-yo-like ups and downs, Carter has at this point alienated the most cohesive and politically conscious segment of the American voting public: the Jewish vote. It is too early to say whether Carter's personal mission to the Middle East to try to revive the flagging hope for a peace settlement between Egypt and Israel can overcome this alienation.

The belief however, is that large numbers of Jewish voters concentrated in states crucial to his reelection will remain antagonistic. They feel that Carter has sided with Egypt's President Anwar Sadat and that he was ready to confront Israeli Prime Minister Menachem Begin with an ultimatum on American-Israeli relations.

Whatever the truth, Begin lent some credence to this when he addressed 2,000 Jewish leaders in New York just before he returned to Jerusalem. He spoke of the very hard time he had had convincing Carter that Israel could never accept the Egyptian demands for a timetable for an independent Palestinian state following the Israeli-Egyptian peace.

"You have great influence," Begin told the cheering audience after saying he had been asked by Carter to sign a "sham" treaty. "Do not hesitate to use that influence."

In Los Angeles, concerned American Jews took full-page newspaper ads to denounce Carter. They timed the ads to coincide with a fund-raising dinner at which Carter could not star because of his decision to fly to the Middle East. As a substitute, Vice President Walter Mondale had a difficult time.

The nominating conventions are 18 months away and a great deal can happen in that time. But despite a widespread belief of a trend to the right politically, Kennedy stands for social advances that have been a mainstay of the Democratic Party in the past and are still the cherished ideals of many.

The last time an incumbent president was denied renomination by his party was in 1884 when Chester A. Arthur was knocked out on the first ballot. Whether this can happen today, when money and television play so important a part, is another matter.