Reagan's first year; Politics: public support still strong; President Reagan at one-year mark: still popular, but growing doubts about his ability to deliver

One year after his inauguration, President Reagan has not exhausted his political mandate for change.

The second Reagan year begins with the economy in recession and with pressure building in Washington to alter his tax-cut plans to create a breakwater against huge incoming federal deficits. His margin of success may prove smaller in 1982.

But the President still enjoys broad public support for the core of his programs. His personal popularity remains strong. He continues to prove the truest believer in his administration's policies - a winning quality among Americans who prefer optimism in its leaders. And his administration's values still seem in accord with the latest conservative norms in social attitudes - with the public again emphasizing traditional family ties, respect for authority , religion's role, and hard work.

''The public is a lot more patient for the effects of Reagan's economic program than are the elites - the press, economists, even some members of his own party,'' says Thomas E. Patterson, director of Syracuse University's Maxwell School of Citizenship and Public Affairs.

''The public is willing to give the President more time,'' Mr. Patterson says. ''They look to the core of policy, not who's minding the store. They see a basic governmental change in Reagan's tax and budget program. They see he may be forced to back off a bit on tax policy. But that would seem secondary.

''The moment of truth is going to be there for Reagan. The public was willing to give Roosevelt eight years. I'm not sure Reagan has four years. But he surely has two years to prove his program will work.''

The Reagan team has made mistakes. An early miscue on social security reinforced a longstanding doubt, preceding even the campaign, about Mr. Reagan's plans for the retirement system. He was caught running the wrong way on the issue of tax exemption for race-biased private schools.

The President's lower standing among blacks and women suggests his appeal is not universal among Americans. On ''fairness'' issues, the President's policies are thought by the public to ''go too easy'' on big business and high-income people, and to be unfair and cause hardship on the poor and the elderly.

The President's standings on most counts are more modest than either his Washington giant-killer reputation for mastering Congress or reports of White House strife and poor performance would suggest.

Americans tend to ''presidentialize'' everything that happens in public affairs, notes Robert Teeter, a Republican strategist. ''We've gone mad presidentially,'' he says of the tendency to try to explain economic, social, and political tides in terms of the current White House officeholder - which tends to exaggerate his actual prospects or impact.

In Mr. Reagan's case, the public is moving toward an even split on his performance. For his handling of the presidency, he actually finished 1981 with fewer supporters and more critics than did Jimmy Carter at the same point. But three-fourths of the public do approve of Reagan as a person, according to the Gallup Organization. And in hypothetical reruns of the 1980 election, there are few second thoughts: Americans say they would favor Reagan again by 2 to 1 over Carter. Still, Reagan's approval rating ended his first year lower than the rating of any president since World War II except Gerald Ford.

While the President's party is having a heyday in Washington, there are few signs of permanent Republican gains around the country. In party identification, the Democrats have reclaimed their 3-to-2 or better edge over the Republicans after a year of Reagan rule. While no fundamental party realignment seems in the works, the public does appear to like some of the Reagan administration's ''new federalism'' themes.

How complex, if not ironic, are political fortunes was suggested this week as Democrat Charles Robb, President Lyndon Johnson's son-in-law, was sworn in as governor of Virginia, across the Potomac. Not only is Mr. Robb a member of another political dynasty, but Virginia's congressional delegation had been one of Mr. Reagan's staunchest backers his first year.

On whether Reaganomics will work, the public may be willing to wait and see a little longer, but it evidently does not expect to see much. Asked whether, as a result of Reagan programs, a year hence inflation will drop below 10 percent, interest rates and unemployment will come down, and the federal budget will be on the way to being balanced, the public skeptically votes ''no'' to all four in the latest Harris surveys.

Such skepticism over results may reflect the public's view of how hard the job is, rather than just a rating on the President's expected performance.

Also, the public wants its presidents to succeed, White House scholars say.