President Carter made a desperate appeal to the supporters of John B. Anderson today as his reelection campaign, shadowed to the end by the Iran hostage crisis, lurched on an uncertain path across the country.

His face gray and puffy and lined with fatigue, Carter pressed his campaign far into the night, arriving here tonight even after the clocks on the East Coast had passed midnight, the dawn of Election Day, and the country began its final judgment on his presidency.

The president canceled a scheduled campaign stop in Los Angeles tonight, all but conceding Republican nominee Ronald Reagan his home state, but continued as planned to the Pacific Northwest, looking for a few more votes in an election race in which he clearly trails.

As he moved from one rally to the next, Carter said nothing about the hostages in Iran, the issue that has lasted as long as the campaign and which remains the great unknown in the election outcome. With the immmediate release of the hostages and his own political survival now largely out of his hands, he turned instead to the supporters of independent candidate Anderson with a last-ditch appeal.

Identifying himself for the first time with an opponent he has steadfastly ignored, the president told the Anderson supporters he shares many of the goals of the Illinois congressman.

"And on the most overriding issue of all, the issue of peace and the control of nuclear weapons and preventing the spread of nuclear weapons, on this great fundamental issue, all of the candidates are on one side and Gov. Reagan is on the other side," he said at an airport rally in Akron, Ohio, this morning. o

As the president's campaign entourage made its way across the country today, the mood of his aides was subdued but not openly defeatist. If Carter faces an almost impossible task in the election on Tuesday, as many analysts believe, few of those around him appeared ready to admit it today.

Nor was the president. "I feel good about it," he said in Akron when asked about the election.

Carter refused to comment on the situation in Iran. Nonetheless, the hostages, as they have been from the beginning, were very much a part of this last campaign day, coloring even its final acts with uncertainty.

When the president left Washington this morning, all that was certain was that he would go to Ohio. The rest of his schedule depended on the events in Iran, his aides said. But the dropping of the scheduled California stop, announced while Carter was flying from Akron to Granite City, Ill., was clearly motivated by political rather than diplomatic considerations.

Instead of visiting Los Angeles, the president flew from Springfield, Mo., to Detroit, hoping to squeeze out a few more votes in Michigan, a state his aides consider winnable, before going on the the Pacific Northwest.

There were few indications today of a public rallying to the president's side as the hostage crisis nears a possible resolution. The crowd at the airport rally in Akron -- Carter's lone campaign appearance this fall with Vice President Mondale -- was disappointingly small. In Granite City, a larger crowd gathered to hear him, but there were boos mixed with cheers when he denounced Reagan as a "right-wing Republican."

There was a certain appropriateness to the day's scheduling uncertainties, for whatever the final outcome on Tuesday, this much could be said as the president pushed himself through the last few hours: things never seemed to go according to plan.

One year ago today, on the day before the hostages were seized, Jimmy Carter looked like a political corpse. But the hostages transformed his reelection chances, just as they would hang over the politics of 1980 all year. r

The president anguished over the hostages, but he never let them cloud his political judgment. In Iowa in January, the politics of the primaries dictated that he back out of a debate with challenger Sen. Edward M. Kennedy (D-Mass.), which he did, arguing that the hostage situation demanded his complete attention.Yet today, with his presidency hanging precariously on the loyalty of Democrats and the doubts of Anderson supporters, he hurtled himself across the country even as the international wires crackled with news of the latest moves in the year-long crisis.

For the general election, the Carter political strategists devised a simple plan. Reagan, the aging, former actor and apostle of right-wing causes, would be portrayed as unfit for the presidency. If the American people had never taken to Jimmy Carter with any enthusiasm, they could at least be frightened away from Ronald Reagan.

But Reagan refused to cooperate with this effort to be portrayed as a dangerous political extremist, and when in frustration Carter escalated his rhetoric, there was a backlash. The president's tactics, rather than his opponent's character and views, became for a time a central issue.

Other factors also worked against Carter. Since Labor Day, he has spent 30 campaign days on the road, visiting 24 states, and a map of those travels provides a vivid picture of the inherent advantages Reagan held to the last day of the campaign.

A huge chunk of the country, stretching from just west of the Mississippi River to the West Coast, was never visited by the president. Most of the West was conceded from the outset as Reagan's base. As for Carter, he had no base, not even his native South. In the critical last week of the campaign, he was forced to return again to the South, fighting to preserve what had been his by right of history and heritage four years ago.

And as the campaign ground through its final days, the president appeared to have little or no base in an even more important sense. In four years in the White House he never learned how to generate enthusiasm for his presidency, never sought to tie himself closely to the Democratic Party.

Always singleminded and determined in his quest, the president pursued the search for as long and as far as he could. It was after midnight on the East Coast when Air Force One left Portland headed for Seattle and the last rally, the last speech, flying over a remote corner of the country that is so different and so far from his native Georgia. He was a long way from home in more ways than one.