The attrition of events has perceptibly weakened Jimmy Carter, who is caught between the leftward pull of the Democratic Party and the conservative drift of the nation. This has led to titillating whispers that Carter is developing the pall of a one-term President.

This prospect may be highly premature, but potential rivals are emerging from the shadows. They are backing into the sunlight, to be sure, protesting every step of the way that they have no designs no higher office. There is a certain strategy behind these folkways, for the first candidate who pokes his head above the crowd risks having it knocked off.

Nevertheless, several hopefuls are maneuvering into position to challenge Carter in 1980. It is possibly too early to assess them, but the advance signs seems to favor two men. Among the Democrats, California's charismatic but enigmatic Gov. Edmund G. Brown Jr. is warming up in the bullpen4. Among the Republicans, the fastest jaw in the West, John Connally of Texas, appears to have gained the inside track.

Brown cannot get it out of his mind, according to close associates, that he beat Jimmy Carter in four out of four primaries last year. The youthful governor believes he can do it again.

He has an electricity that supercharges his followers, an integrity that approaches austerity, a simplicity that baffles the political sophisticates. He embraces his party's predilections just enough to keep the professionals in his corner, yet he maintains an aloofness from the old Democratic powers and panaceas. He has a venturesome mind that stirs the visionary. Yet because of his cost cutting and good management, he doesn't offend the practical.

Ironically enough, Carter and Brown have many qualities in common. Both take a moralistic approach to government. Carter the born-again Baptist and Brown the erstwhile Jesuit seminarian. There is something ambiguous and remote about them, yet both seem to have touched the wellsprings of America. Both men have tended to by-pass, even oppose, the Democratic Party's traditional bastions and bring their own constituencies into the fold.

Brown is now preparing himself for bigger things, venturing quietly into the foreign field with trips to Japan and England. He has also established contact with Soviet Ambassador Anatoly Dobrynin. Characteristically, Brown has paid for his own travel on the cheapest available transportation.

In contrast, John Connally combines the blustering amiability of a Lyndon Johnson with the used-car sales tactics of a Richard Nixon. Connally looms on the Republican horizon, a Texan among Rhode Islanders, a leader who always seems sure of himself, who tends to overpower those who stand in his way. He has great abilities and great faults.

Only Connally would try to turn a bribery trial into a political asset. With characteristic bluff, he has contended that his integrity has now been proven in court. Certainly, no other presidential contender can boast an acquittal for such serious charges.

The jury, true enough, found Connally innocent of taking a $10,000 bribe from the milk producers. There were no witnesses to the alleged bribe, and the jurors, quite properly, gave him the benefit of any doubts.

But the court record still contains a damning taped conversation between Connally and Richard Nixon. Connally told Nixon that the dairy men were "amassing an enormous amount of money that they're going to put into political activity, very frankly."

The blunt Texan, then Nixon's Treasury Secretary, advised Nixon to grant the dairymen a price increase. "If you don't," said Connally. "you've cost yourself some money." Later, he stressed again: "You're in this for everything you can get out of it."

It took the jurors more than five hours to agree upon Connally's innocence. The jury foreman. Dennis O'Toole, announced after the trial: "Our verdict meant not that we had found necessarily that John Connally was innocent but, rather, not guilty based on the case presented to us."

This might seem a poor foundation for a presidential campaign. Yet Connally has amassed more campaign funds and political IOUs, according to party sources, than any other Republican contender.

There is a presidential aura about Connally, this rustic sophisticate, who radiates charisma and cordiality. Yet there is also a slight taint of Watergate, Carter's personal pollster found in a past poll that Connally "is rated very unfavorable by Americans overall and even by many Republicans. Clearly, the residue of scandal has outlasted the news of his acquittal on the actual charges brought against him."