An hour before President Carter went before the cameras yesterday to answer questions at his 27th press conference, one of his top aides remarked, "He's got an awful lot of pressure on him."

For 35 minutes, Carter was challenged to say how he hoped to deal with problems from the Horn of Africa and the Middle East to the coal mines of West Virginia.

He was pressed to explain and defend his policy on Rhodesia, the decline of the dollar, the price of natural gas and the tax rates on middle-income families. He was cross-examined on the presonnel practices of the Justice Department and the resignation of his own political aide, Mark Siegel.

The reporters did not begin to exhaust the catalogue of tough questions now converging on Carter in his 14th month as president.Time ran out before anyone could ask him about his embattled Panama Canal treaties, or about the threat to his human-rights policies embodied in the Belgrade communique and the reports from Moscow that Anatoly Scharansky may be tried soon as a traitor.

Nor were there any questions on the issue his advisers regard as perhaps the greatest threat to his political position - the resurgence of inflation, symbolized by yesterday's announcement of the sharpest jump in the wholesale price index in 39 months.

Carter's demeanor during the press conference was as serene as always. He looked on the cheerful side of every problem, expressing confidence that the Cubans and Russians would clear out of Africa as alacritously as he hopes te striking miners would return to their jobs.

"He doesn't look on these as bad times," a presidential assistant said. "He likes the challenge, but it will be good for him to get some of the pressure off. He's got an awful lot of balls in the air at once."

As this last comment suggests, there is an accumulating sense within the White House that the man they all for is about to undergo a rapid-fire series of tests that will, in all likelihood, stamp him as a winner of a loser in the eyes of the American voters and, perhaps, even in the judgment of history.

The most important visible, and perhaps the most important, of those tests is next Thursday's Senate roll call on the first of the two Panama Canal treaties. Yesterday Carter's chief lobbyist, Frank Moore, pronounced himself "a lot happier with the prospect than I was two days ago," apparently refecting the intensive discussions that have been taking place with undecided senators.

But no one in a position of responsibility at the White House is prepared to claim that the 67 votes for ratification are in hand. And in the office of Hamilton Jordan, the president's chief aide, a broadcast of the Senate debate has replaced the accustomed stereo music as the background for conversations.

The uncertainty of the canal vote is symbolic of the suspense enveloping almost all the major, unresolved questions now surrounding the Carter presidency.

Many of the major initiatives launched in the optimistic early days of the administration have come to a head at once. The time has arrived when Carter will either deliver on his commitments or not. He has discovered that, in most cases, the decisions rests largely in other hands than his.

When the president said of Israeli Premier Menachem Begin - whose visit here next week may well prove crucial to Carter's quest for a Middle East peace settlement - is equally true of many others who now hold Carter's political future hostage.

"He is a very strong and independent person," the president said of Begin. "I don't have any intention to pressure (him). I don't have any desire to do it and couldn't if I wanted to."

What is true of Begin is true of the humblest miner in the coalfields of Kentucky, whose willingness to accede to the president's back-to-work order is yet another of the current tests of Carter's authority and political potency.

When an aide was asked what, if any, steps the White House was taking to improve the chances for compliance with the Taft-Hartley injunction, he shrugged as if to suggest th futility of such an effort. "We know there's going to b a lot of anti-administration rhetoric," he said, "but in the long run, we hope they'll see that taking a contract makes sense."

Critics of Carter's performance assert that all too often he has failed to marshall his forces behind his own initiatives, leaving himself with nothing except hope to be applied toward achievement of his goals.

But, in the eyes of his associates, the difficulty is deeper than that. They see the president as a man who has come to office at a time when the resources of presidential leadership are meager, when measured against the toughness of the problems that Carter has chosen to challenge.

Comprehensive energy legislation, a Middle East peace settlement, easing the strain in Panama relations, bringing stability to the coalfields, finding a peaceful transition to black rule in Africa, controlling inflation - these are goals that eluded previous presidents, who governed at a time before Watergate and Vietnam had eroded the authority of the Oval Office and before Congress had become the independent, assertive body it is today.

But that rationale is of little political relevance to Carter, who campaigned on the explicit promise that he had the courage, the independence and the know-how to solve these long-accumulating problems.

Almost every poll being read in the Whit House htese days meausures a growing public skepticism that Jimmy Carte is up to the job, that he can deliver on his promises. His job approcal rate in the latest NBC-Associated Press poll, for example, was about half as high as it stood a year ago.

That is why the pressure for a "big win" is almost palpable in the White House these days. In one sense, it is still early in the Carter Administration. But in another, time is running out on his opportunities to demonstrate that he can achieve some positive results.

Somewhere in that long list of tests coming up in the next few weeks, Carter - in the view of his own associates - has to score a breakthrough. If he does not, he may be a long time waiting for another chance.