It had been only 361 days since America last elected a President, and it would be exactly 1,100 more until the next time - yet here was John B. Connally on the 29th day of the month making his 19th speech of the month.

He had squeezed six abreast on a jetliner, had been splashed on from the flight attendant's cart and had carried his own luggage through vast airport concourses. The travelling took the better part of the day, and even before it was over. Connally turned and said, "What was it Mondale said, he didn't want to spend the rest of his life in hotels?"

All to speak for 35 minutes to a chicken-fed audience at the Western Republican Conference. But when he was done, Tess Gregor of the Utah State Central Committee shook the hand of the silver-haired Connally and delivered the results: "I didn't think I'd like you, but today I fell in love with you."

In many minds there is little doubt what John - Big John - Connally is up to. "Well, he's running for President ," concludes Richard Richards, the state party ex-chairman who rebuilt the Republican Party in Utah.

Yet Connally, who last month announced the formation of a political action committee with a $1 million fund-raising goal, answers the question with less committment. He sayd simply, "I don't know how you stop that assumption. The alternative is for me to do nothing to retire from politics."

Connally assures that no decision has been made on 1980, that he is working only to increase the number of Republicans elected to the nations' statehouses, gubernatorial mansions, and Congress next year.

"Seventy-eight will be the crucial test of whether the mood of the country is what I think it is," he said. And only then will a decision follow.

His current efforts, however - raising funds to finance his activities, to meet Republicans everywhere and to distribute to next year's candidates - are crucial to that.

"If he's going to be a candidate," says Keith L. Brown, Colorado national committeeman from Denver, "he's certainly has to be doing what he's doing now."

Connally even professes mixed feelings for the office. He is after all, the man who as governor of Texas was riding in front of John F. Kennedy when he was killed, the man who saw his fellow Texan and close friend Lyndon B. Johnson virtually driven from the presidency, and the man who as Secretary of the Treasury and then-newly converted Republican saw Richard M. Nixon disgraced.

He is a man then, driving toward the presidency but one who claims not to be driven to it. The road last month alone took him to such places as Pittsburgh on Tuesday, Las Vegas on Thursday, San Diego on Friday. There were morning speeches and dinner speeches, a talk to the National Welders' Supply Association, one to the Republican Governors' Conference.

There is the flash of recognition from individuals as he walks the airports: a man from La Jolla who looks like Mickey Rooney and who is wearing leopard-sking-print pants offers his support. Indeed, as Connally was announcing the formation of this "John Connally Citizens Forum," the Gallup Poll was declaring his the third-most recognized name among the already mentioned candidates for the Republican presidential nomination in 1980.

But he is sensitive, too, that so much of the recognition is attached to the Nixon, years. He slapped at a Denver newspaper which likened his off-year stumping for the party and for other candidates to Nixon's of 19766, and said: "Baker's doing it. Dole's doing it, Reagan's doing it, but I'm the only one who's doing it like Nixon ."

Of his acquittal by a federal court in Washington, D.C., on bribery charges, Connally says, "Only the media mentions it," and that if it should arise in any campaign he will deal with it then.

That is not the only potential problem for the 60-year-old Connally. A Democrat until 1973, he has never held office as a Republican, and his own state party still containes activists who remember the days when Connally defeated them soundly as a Democreat.

And unless the state legislature changes the law. Texas Republicans will choose their presidential nominee by convention in 1960, giving the hard-time activists more control than in an open primary.

Too, he is a figure from an older generation of political leaders and one who served an administration that disintegrated into scandal, and is a time when many Republican leaders think the party needs younger candidates representing a break from the past.

But not everyone shares that view, and it was in part the freshest of speaking requests washing through Connally's law office that he says prompted him to create the "Citizens' Forum." Appearances, in many cases, were too close together in time and too far part in space. Travel was inefficient. The opportunity to prepare new speeches was limited.

"For the last three years, I've traveled the country on my own, basically without assistance, trying to stir enthusiasm for the Republican Party in a non-professional way," Connally said. "It's enormously difficult and hard work."

"I decided if I was going to do it. I needed to do it so maximize the efficiently and the effect," he said.

So today he has a full-time staff aide for the forum with an office and a secretary in Houston - "a small staff," he call sit, "to take care of the invitations and the telephone calls" and to insulate him from the pressures of clients and friends making special pleadings for an appearance by John Connally.

Connally is one of the party's most accomplished fund-raisers, and his goal is $1 million to finance his staff operations, his travel, research and speeches. He says that what is left will go to Republican candidates.

The research, he says, is intended to provide new ideas for the candidates for the party and to carry the message that in the 1970s Democrats have become the party of the status quo.

He now calls the Democrats the party of retreat, regression, resignation. He charts a course for the Grand Old Party to stand for growth, optimism and prosperity. It is a message well-received by Republicans, and as Connally spoke here several guests - both at the head table and in the general audience - whispered observations of "he's good" and "I think he's really good."

Not bad for a man described by Utah Republican Richards as "essentially an unknown.

Although Richards is on the state steering committee for Ronald Reagan, he adds, "I'm looking at him [Connally] myself."

Another Republican describes the West now as Regan and Connally country. They take it as a given here that the West, which voted for Gerald R. Ford last year, is already Republican country.

Thus Connally and Reagan may find themselves trying to harvest the same food. "Of course, there is some jockeying," said Republican National Committee Chairman Bill Brock, "but they're not running against each other." He claims that Republicans "just can't do anything but gain" from their efforts.

Mary Crisp, the national committee cochairman, goes so far as to rule out of the 1980 presidential picture both Regan, who will be 69 for the next election, and ex-President Ford. Her conclusion is that Connally is exploring the possibility of a candidacy, "and justifiably."

But, she cautions, "political changes so quickly. People come and people go."

For now, though, Connally, a man described as charismatic, powerful and dynamic, is just on the go. He laments the inability to spend time at his Texas ranch, and the trips that take him far from his No.1-ranked Texas Longhorns football team.

It was just such a life that led them-Sen. and now-Vice President Mondale in 1974 to withdraw from the presidental decathlon because, in the words of an aide, "he didn't want to spend the next two years in Holiday Inns."

So when Connally quotes Mondale on running for the presidency may be more on his mind than 1978.