It is curious but not inexplicable: 1968 was perhaps the worst year in American history, yet it is a year for which many people are nostalgic. Recollected in tranquillity, the politics of 1968 seems painted entirely in primary colors, with large heroes and lurid villains. For many participants it was a year agreeably free of ambiguities and impure alliances.

Two decades on, presidential politics seems, to some people, tame to a depressing degree. The Democratic side calls to mind this judgment of a book reviewer: ''A generous, sensitive, intelligent, humane and literate book that despite its generosity, sensitivity, humanity and literacy manages to be a deadly bore.''

However, the Democrats could give us this year what they once specialized in -- a stimulating convention. So it is timely to tell a story that began with a 3 a.m. telephone call on a Sunday morning in Chicago two decades ago.

It was the Sunday before the Democrats' convention was to open and Robert Strauss, Democratic national committeeman from Texas, was sleeping the sleep of the just in the Conrad Hilton Hotel, in a suite overlooking Grant Park, which was a campground for the anti-war movement. At 3 a.m. Strauss was awakened by a call from Walter Jenkins, a former aide to Lyndon Johnson and a friend of both Strauss and Eugene McCarthy.

Jenkins said the McCarthy campaign wanted to reach Texas Gov. John Connally. Strauss, whose suite was next to Connally's, dozed fitfully until 7 a.m., when he received a call from Richard Goodwin, a senior McCarthy aide. Goodwin said he was in McCarthy's suite and that McCarthy needed to talk to Connally about something important. Goodwin was invited to the Texans' floor.

Connally, a leading hawk, was President Johnson's voice at governors' conferences and elsewhere. He was emblematic of the Democratic Party establishment. He, Strauss and Goodwin began by swapping political gossip and war stories. To their surprise, Connally and Strauss found Goodwin great fun.

Then Goodwin got down to business, saying that McCarthy wanted to make a deal.

Connally was, at the moment, mad at Hubert Humphrey, who, in an attempt to appease liberals, had gone back on his promise to support retention of the unit rule for delegations that wanted it at the 1968 convention. But Connally was not mad enough to go for Goodwin's idea.

It was that Connally endorse McCarthy before the convention opened the next day, in exchange for which McCarthy would choose Connally as his running mate. Furthermore, Connally would be given considerable patronage power including the right to select some Cabinet and judicial nominees.

Strauss remembers that Connally, whose life in Texas politics had not left him with delicate sensibilities, was ''shocked by the cold-bloodedness'' of the proposition. But Connally said he could not consider it. When the meeting ended, Connally came into the room where his wife Nellie and Helen Strauss were waiting. He kissed Helen and told her that her husband had just missed out on appointment as chief justice of the Supreme Court.

McCarthy, who never talked to Connally, says that whatever Goodwin did with Connally was done without consulting him. The deal does not sound like McCarthy, whose philosophic fatalism was like that of Arthur Balfour, who, when he turned away from party leadership, was explained by a friend: ''He knows that there once was an ice age and that there will be an ice age again.''

However, McCarthy was not severely liberal on domestic policy, and in his days on the Finance Committee he had often been helpful to Texas interests. Furthermore, Goodwin was a very busy boy that year, having worked for McCarthy in New Hampshire, then Robert Kennedy, then McCarthy again. There were many marshals' batons in his knapsack.

Today Goodwin denies such a deal was proposed. He says he only stressed that by supporting McCarthy, Connally could become the third Texan to help a northerner become president. (Of course the other two, Garner and LBJ, became vice presidents.)

Well, memories vary. Here I trust the Texans'.

Certainly, when a presidential nomination is on the line, some political people will think the hitherto unthinkable and will find themselves capable of remarkable elasticity. We might see some of that this year, if the Democrats cannot settle things before their convention.

Their contest -- which is, after all, about control of nuclear weapons, prevention of financial panics and other important things -- currently reminds one of the book review that said, ''It is curious how incest, impotence, nymphomania, religious mania and real-estate speculation can be so dull.'' But this year, as two decades ago, the convention could be an interesting chapter.