"America is back," President Reagan proclaimed during the 1984 campaign, and a majority of his countrymen agreed with him. Optimistic young people deserted the Democrats and flocked to Reagan's banner. Displays of patriotism became fashionable again.

Neither Reagan's optimism nor his popularity has diminished in the year since his reelection. Bolstered by new U.S. overtures to the Soviets and the capture of the hijackers of the Achille Lauro, the approval rating for Reagan's conduct of foreign affairs has soared to record levels. Reagan has gained popular support in the first year of his second term, usually a period in which presidential fortunes decline.

But is "America back," in the more profound meaning of that phrase? Has the nation shed the cynicism that marked the Vietnam war and Watergate days of the mid-1970s and recovered the historic sense of optimism long regarded as the most distinctive national characteristic?

The customary answer to these questions is affirmative and not just from Reagan. But this conventional wisdom is challenged by surveys suggesting that the fabric of trust torn by Vietnam and Watergate remains unrepaired.

In July, a Washington Post-ABC Poll asked Americans how much they trusted "the government in Washington to do what is right." Six of 10 persons answered "only some of the time" or "never." Slightly fewer than four of 10 said "most of the time" or "always."

Contrast this with the level of confidence Americans displayed in their government as the Vietnam war escalated in 1964. In that year, when Lyndon B. Johnson won on a peace and prosperity platform, the University of Michigan Survey Research Center found that 76 percent of the people expressed a high degree of trust in government "all or most of the time."

A few months ago, pollster Louis Harris found that 56 percent of Americans feel alienated from the U.S. power structure and that 76 percent agree with the statement that "the rich get richer and the poor get poorer."

Last January, a survey by the University of Chicago's National Research Center also contradicted the prevailing view that Americans are as incurably optimstic as their president. A majority of those polled thought that "the lot of the average person" was getting worse. And four of 10 persons agreed with the rather extreme statement that "it's hardly fair to bring a child into the world with the way things look for the future."

These findings reinforce the view of Reagan advisers that he is popular partly because many people do not regard him as a politician. Those who see Reagan in political terms perceive him as trying to reduce government's role, a commendable position to those who do not trust their representatives.

Examining Reagan's popularity in the context of the low level of trust in government, Washington Post pollster Barry Sussman believes that the president is confronted with an unusual political opportunity on the major items of his foreign and domestic agenda.

While most Americans are skeptical of government, they worry about the lethal power of the nuclear arsenals of the two superpowers, and they approve of Reagan's determination to improve relations with the Soviet Union. If the president's meeting with Soviet leader Mikhail Gorbachev is seen as reducing tensions and the likelihood of nuclear war, his popularity could soar.

The sleeper issue that also could benefit Reagan is tax reform, which may be rescued from White House ineptitude by a Democrat, House Ways and Means Committee Chairman Dan Rostenkowski. A majority of Americans believes that the tax system is unfair and, in Sussman's view, would consider a true tax reform bill an act of justice.

Whether Reagan's tax overhaul will pass or meet this test is anybody's guess. A summit that reduces nuclear arsenals is even more problematical. But, if Reagan succeeds in either arena, it may be true, as he often said in 1984, that "you ain't seen nothing yet." Perhaps some of Reagan's success, if it comes, will rub off on the system.

Reaganism of the Week: Speaking to religious leaders Tuesday, Reagan said: " . . . The Lord has told us that his share is a tenth of what we earn and He has told us that, if we prosper 10 times as much, we will give 10 times as much. But when we start computing Caesar's share under our present tax policy, you can prosper 10 times as much and find you're paying 50 times as much tax . . . . What's fair for the Lord ought to be more reasonably fair for Caesar, also."