As the 97th Congress gets under way, it could well ask itself why the American people repeatedly hold the legislative branch in such low esteem, with confidence ratings as low as 19 percent.

Congress can hardly be unaware that the opinion polls regularly find it and the U.S. public far apart on numerous fundamental issues. So what becomes of representative government when the apparent will of the people is consistently thwarted by their elected officials?

Interest in this troubling question has been quickened by several highly publicized murders that have focused renewed attention on the unrestrained sale of handguns in the United States. For years, the public has strongly favored legislation to control these weapons while Congress has repeatedly rejected all efforts at reform.

That, however, is only one relatively minor example of the frustration the public has endured in recent years, and no doubt will continue to endure during the life of the incoming Congress. The list of differences with Congress is long and formidable.

One of the immediate, pressing problems confronting the president-elect and Congress is inflation. Right or wrong, the public is decisively for wage and price controls, as it has been for years. On the other hand, both the major parties and their leaders are adamantly against controls, although the politicians have failed to offer a practical alternative. In the presidential election, the popular vote and the electoral college vote, as often in the past, bore little relation to each other, which is one reason the public has repeatedly clamored for abolition of the electoral system. Nevertheless, through filibusters and other obstructive tactics, Congress has circumvented all efforts for change, just as it has ignored popular demand for a national primary to supplant the endless state primaries.

As soon as the Reagan administration takes office, it will have to deal with the national budget and the makings of another huge deficit, despite public opposition to move red ink. For years, U.S. voters have even backed a constitutional amendment making a balanced budget mandatory. That may be misguided, but it is another example of the public's will being disregarded.

No matter how large the prospective deficit turns out to be, it is taken for granted that Congress will soon enact a large tax cut, although the polls indicate there is no popular demand for it. Quite the contrary. Several weeks ago, the ABC-Harris poll showed a 55-to-41 stand against cutting the income tax. An NBC-AP poll flatly reports that "Americans do not want a cut now."

Even after the Russian invasion of Afghanistan, the public continued to support SALT II, but Senate hostility was such that President Carter put it in cold storage where it remains. Although the American people acclaimed former president Nixon's detente with Russia, Congress passed the Jackson-Vanik Amendment killing Nixon's trade agreement with Moscow, regarded as a cornerstone of detente.

Unlike Congress, the public long ago made up its mind on how to deal with illegal aliens. It definitely wants identity cards to prevent the hiring of workers smuggled into the country. Congress, however, continues to temporize on this and other solutions, while the situation further deteriorates.

The president-elect and his party endorse a constitutional amendment outlawing abortion, but the public doesn't. Reagan's budget advisers are talking about cuts in food stamps, medical care and educational grants, yet the polls show unwaivering popular support for these programs.

It will be illuminating to see what Congress and the incoming administration do about further government subsidies for the stumbling Chrysler Corporation. So far, Chrysler has succeeded in getting huge federal guarantees even though polls report the public is 7 to 1 against that kind of a rescue.

In the light of all these disagreements, it may well be asked how such a large majority of senators and representatives manage to win reelection time after time. One veteran congressman who has been reelected a dozen times thinks the conflicts are more apparent than real.

"Just remember," he says, "that we congressmen know our districts pretty well. We can usually tell when the folks mean business and when they're just sounding off. We don't have to rely on national polls, for most of us regularly poll our own districts." The first thing to keep in mind, he says, is that the polls shouldn't be taken too literally. Voters, he says, seldom have much knowledge about, or interest in, many of the issues on which they are questioned, but they still don't hesitate to volunteer offhand opinions.

The polls, he thinks, tend to exaggerate both the breadth and depth of the reaction on national and international issues. My consultant said he realized there was popular support for SALT II, but he also was aware that a national survey found that 77 percent of those polled could not identify the two countries involved.

"Don't forget," he said, "that the voters are human: they like to have their cake and eat it too. They are against big spending, but you better not cut their favorite programs. The congressmen who last are the ones who learn to reconcile these contradictions. That's how over 90 percent of the incumbents usually get reelected."