If history is any guide, then the big political question of 1980 is whether Jimmy Carter's fate is going to match that of incumbent president Herbert Hoover in 1962 or of incumbent president Harry Truman in 1948.

Both were clearly underdogs at this point in their uphill campaigns. Hoover went on to a shattering repudiation while Truman pulled off the political miracle of the century. Are there parallels today?

The Gallup Poll currently shows Carter's popularity at only 21 percent, the lowest for any president since Gallup began such measurements of opinion in 1940. In June 1948, Truman had a 69 ppercent approval rating (three and a half years later he sank to his low of 23 percent). If Gallup had been polling in the summer of 1962, it is probable that Hoover's rating would have been closer to the Carter 21 percent than to Truman's 39.

Looking back at the 1932 and 1948 campaigns, it is clear that the attitudes, personalities and policies of the incumbent presidents had more to do with the November outcomes than did the strength of their challengers.

In 1928, Herbert Hoover, an acknowledged able administrator with wide experience at home and abroad, easily rode the tide of Coolidge prosperity into the White House. But the roof fell in less than a year later, signaled by the stock market crash of October 1929. In the next three years, banks began to fail and close, there were raids on the dollar, businesses went bankrupt, farms were foreclosed, food riots broke out in cities, and by 1932 federal workers were forced by Congress to take payless furloughs or accept salary cuts of up to 20 percent. Unemployment figures were sketchy, but probably a fourth of the work force was jobless.

At the Republican convention in Chicago, there was little enthusiasm for Hoover's renomination, yet he won on the first ballot with all but 27 1/2 of the 1,154 votes. A measure of the Hoover managers' jitters, however, was the rough way in which one rival candidate was dragged off the floor when he tried to withdraw in favor of ex-president Coolidge.

Hoover believed, and Republicans generally agreed, that relief for the jobless was a local responsibility or, at most, a task for the Red Cross. He feared the growth of the federal government because "where people divest themselves of local government they at once lay the foundation for the destruction of their liberties."

Hoover increasingly endured sullen looks, eggs thrown at his campaign train and ridicule when he said, as he did whenever it appeared the Depression might be moderating, that prosperity was just around the corner. The ultimate sign of contempt was the term "Hooverville," applied to the shantytowns of the unemployed erected along railroad tracks and in city dumps.

Hoover was a beaten candidate in spirit from the campaign's beginning. By contrast, his challenger, Franklin D. Roosevelt, is acknowledged as the most magnetic political leader of the century. But in 1932, Roosevelt was widely viewed as no more than a politician with no real program, simply hungering for the power of the presidency. Walter Lippmann and H. L. Mencken dismissed him as inadequate for the task. In November, FDR swamped Hoover by seven million votes. Hoover's total fell more than five and a half million below his vote of four years earlier, as more than a quarter of those 1928 votes shifted to FDR--votes cast more against Hoover than for Roosevelt. In short, Hoover lost the election more than FDR won it.

It was the other way around in 1948, when Truman won the election more than Thomas E. Dewey lost it. After having lost to FDR, "the champ," in 1944, Dewey was so sure of victory this time that he took the high road. He fatally ignored a rebellion in the Farm Belt against his party after the Republican-controlled Congress had limited government-financed storage bins for what turned out to be a bumper harvest that year. In May, a Gallup trial heat had Dewey at 49 percent and Truman at 38 percesnt; by August, Dewey had added a point, with Truman losing one.

In between , came the attempt to deny Truman renomination, a move not dissimilar to the current effort against Carter. Such prominent Democrats as three of FDR's sons, then-Minneapolis Mayor Hubert Humphrey and Sen. John Stennis wanted to dump Truman, and some of them, and many others--including Americans for Democratic Action--called for drafting Gen. Dwight Eisenhower or Justice William O. Douglas in an "open convention."

By then, Truman had been damned for everything from adding a balcony to the White House to advocating civil rights legislation and threatening Stalin with war over the Russian blockade of Berlin. Labor leaders and liberals at one end of the old FDR coalition and conservative Southern Democrats at the other were equally disgruntled. At the Philadelphia convention, described in The Washington Post as a "wake," Truman was nominated on the first ballot with 947 1/2 votes to 263 for Sen. Richard Russell of Georgia and half a vote for ex-governor Paul McNutt of Indiana.

Before that vote, the convention had been torn apart in a fight over a civil rights plank, won by the liberals, that led to a Southern walkout and formation of a Dixiecrat ticket headed by Strom Thurmond, who was then Democratic governor of South Carolina. On the left, Henry Wallace, FDR's second vice president, ran as a Progressive, though his campaign was essentially captured by the communists.

It seemed, as Clare Boothe Luce had told the GOP convention, that Truman was "a gone goose." Yet despite Dewey's record and his rich baritone voice, he did look "like the little man on the wedding cake," as Alice Roosevelt Longworth's dentist had said to her and as she had happily repeated.

Truman's acceptance speech was delayed until 2 a.m., telecast to a limited audience on the East Coast since there was as yet no national hookup. However, the speech electrified the convention and set the tone of attack that came to be known as the "give 'em hell, Harry" style.

Truman was a monotonous speaker when he read a manuscript, peering through thick glasses. His young White Houseaide, Clark Clifford, had advised him to do two things: throw away the prepared speeches in favor of highly personalized campaigning, and invoke the"magic" of the White House, the power of the incumbent to favor and flatter. Truman did both, just as Carter is trying to do.

Truman repeatedly assaulted that "terrible 80th Congress" controlled by the Republicans, and he castigated the voters for having elected it. He oozed self-confidence throughout the campaign, though many thought it only a pose, and he carried the fight across the country in spectacular "whistle stop" campaigning. Increasingly, he ran more against Hoover than against Dewey. Truman privately predicted 340 electoral votes (he got 303), but the pundits, polls and press were almost unanimous that he would be thrown out of office just as Hoover had been. The final Gallup Poll gave Dewey the edge by 49.5 percent to 44.5.

Truman's win with 49.5 percent of the popular vote to Dewey's 45.1, with 2.5 percent each for Thurmond and Wallace, is deceiving in that a shift of only a few thousand votes in Ohio, Illinois and California would have elected Dewey. If Dewey had won only two of those three states, the election would have been thrown into the House. Thurmond won 36 electoral votes; Wallace didn't win any, but his votes did deny Truman New York, Michigan and Maryland. Furthermore, in 1948 there was a widespread "plague on both your houses" attitude toward Dewey and Truman. Despite the alternative choices of Wallace and Thurmond, the total vote cast fell over 1.1 million below the 1940 total, although the voting age population had grown by 11 million.

Today, President Carter's troubles with the economy and foreign affairs seem more like Hoover's troubles than Truman's, although the economy is certainly a far cry from that of the Great Depression. On the other hand, Carter's tenacity of purpose and demonstrated campaign abilities, while in sharp contrast to much of his handling of the presidency, resemble Truman's doggedness and self-assurance rather than Hoover's attitude of resignation. However lopsided the Reagan-Carter contest appears on the eve of the Democratic convention, it would be risky to assume that Carter is certain to suffer the disaster that was Hoover's rather than pull off the miracle that was Truman's.