Based on popularity polls alone, Jimmy Carter's presidency would seem to be in the deepest trouble, no matter what he says tonight in his speech and no matter what he does in the next few weeks and months.

There is a deepening mood of pessimism amont the voters about the country's future, about their own economic futures, and, more immediately, about the government's ability to make things right # under President Carter's leadership.

In this dismal context, however, most professional political analysts are not about to write Carter off. He is still a visible candidate, they say, a force to be reckoned with.

His approval rating is terrible. But he is liked, and as a man, he is trusted. Head to head with other presidential contenders, he doesn't do nearly as badly, and on the issues he is pretty much in tune with the electorate.

By next month, however, the analysts, most of them pollsters, concede that they may have changed their minds. They agree that his performance now is absolutely critical. There is a good chance it could break him politically.

But they see an equally good chance that it could make him. More than the Mideast talks, more than SALT, this is the crucial fork in the road.

Most observers agree that Carter must strive for one specific achievement in his speech tonight and in the months to follow: he must give the appearance of being an able leader.

More than anything else, the pollsters say that people want someone to do something.They care almost as much about that as they do about just what it is that get done. For many, "doing something" is the very essence of leadership.

The fact that Carter still has any hope at all, in the view of some pollsters, is in part the result of the one constant of public opinion throughout the Carter presidency: he is not viewed as an ordinary politician.

Even as his approval rating has tumbled in the mid- and high 20-percent range, he has been regarded consistently by between 60 and 80 percent of the voters as a man of high moral principle.

That is why Tully Plesser, whose polling firm, Consensus Inc., advises the Republican National Committee, has been telling his clients that Carter may not be as vulnerable as supposed. Donna Kinwell, vice president of V. Lance Tarrance and Associates, which works for Republican presidential candidate John B. Connally, makes a similar point.

""The weaknesses they observe are not those of a political president protecting his personal interests," Plesser said, "but those of a well-intentioned amateur. The opportunity is there to stage some sort of political recovery by demonstrating that a well-intentioned amateur can become a well-intentioned professional.

"The opportunity would not be there if he were perceived to be a political manipulator whose decisions are based on self-interest or partisan politics."

"There is a lot he can do," agreed Democrat Peter Hart, president of Peter D. Hart Associates. "While professionally his job rating may be as low as Nixon's, there is no animus towards the president. The key problem facing him is not his direction on the issues or how voters perceive it. It is his ability to handle them effectively."

This is one of the striking ironies of Carter's political plight. Perhaps no other political figure has as sure and certain a grasp of public opinion. On issues such as tax reform, government reorganization, morality in government and in his occasionally slashing attacks on special interests, Carter's positions could easily be taken from a computer printout showing how the great majority of people feel and what they want from government.

But presidents are judged on performance. That is a cardinal rule in American elections. The polls show that Carter is admired by most Americans for his character and inegrity, but is regarded as an ineffective leader, vacillating, uncertain, amateurish.

"The problem is not so much the words he says," said Ronald Reagan's pollster, Richard Wirthlin, president of Decision Making Information Inc., "but whether he can convey the impression he's in charge and exercising leadership and that leadership can change things. When basic needs are not satisfied, we react very emotionally. If Carter is to restore confidence in his leadership, he has to appeal at that same gut level and confince them that, through his agency, things will improve."

The energy problem, the crisis of the moment, heightens both the opportunity and the risk for Carter, the polls suggest.

More than inflation, often regarded by voters as a bigger problem not subject to solution by any president, energy is something people believe can be "sorted out. Most people find that inflation is a very ugly problem, but they don't think anybody can solve it," said Donna Kinwell, of Connally's polling firm. "With energy, there are very tangible things they can see occurring or not occurring."

There is also hope for Carter in the fact that public opinion does not appear to blame him for causing the crisis, though they hold him responsible for not solving it. A June NBC/Associated Press poll, for example, found that 72 percent held the oil companies and the oil-producing countries responsible for the gasoline shortage, while only 4 percent blamed Carter.

On the other hand, Carter's hope that, as the gas lines grew, the majority of the people would see the energy shortage as real has not yet been fulfilled. In the NBC poll, 65 percent still felt that "it is a hoax." Gallup produced similar results.

Most professionals say that on the energy issue and inflation, in particular, Carter must change the current perception of his presidency as a "passive" effort and convert it to one that appears to be taking bold steps.

That conversion, should be choose to attempt it, will inevitably be made more difficult by a Congress he cannot control. Carter has long threatened to go over the heads of Congress to the people.

At Camp David, he has in a sense created his own Congress. He summoned selected people from Capitol Hill to the Catoctins, but highlighted consultations with governors and private citizens. Whether he chooses to or not, the president is now in a position to announce that he has convened some of the best thinkers in the nation and is presenting programs in line with their views.

Most of the pollsters agree that is will be necessary to produce not just a change in image but real results. With worsening inflation, that, too, may be beyond Carter's control.

Beyond that, the public mood that has fed Carter's decline is a documented phenomenon of the past decade or longer. It has been accompanied by lowered voting turnouts and what one polling firm calls a growing sense of deep and serious trouble" in the country that no president may be able to handle. CAPTION: Graph, The President and the Polls, By Bethann Thornburgh for The Washington Post