Washington — The slide in President Reagan's popularity, which has followed the economy's descent into recession, may have about bottomed out.
Like the economy, where an upturn is expected this summer, a modest recovery in Mr. Reagan's approval rating could lie ahead.
The Falklands controversy in the South Atlantic could work in the President's favor, some opinion analysts say, as Reagan, Britain's ally, associates himself with the theme of the free world asserting itself. The risk is that as hostilities deepen, the public may link Reagan with its unease about involvement in war, a persistent problem for the President.
At home, the President's aides rally to counter negative impressions of a rich man's presidency, or of a willful ideologue in the White House who has pushed budget negotiations with Congress to an impasse.
Trips to Knoxville, Tenn., for the world's fair last weekend, to a black family's home in a suburb outside Washington, D.C., in recent days, and to the heartland state of Illinois to visit his old college haunts next week -- such outings are meant to portray a more caring Reagan, in touch with the common man. His speech to the nation last week and a White House session with GOP congressional leaders this week were meant to show a president who wants to accommodate opponents without caving in on his principles.
In early June Reagan travels to Europe for a round of economic and NATO alliance summitry -- stopping at Versailles, the Vatican, Berlin, and London -- with opportunity to dominate the evening news for a fortnight.
Such orchestrations of the Reagan image ultimately might have limited impact. The performance of the economy and international events will have the greatest bearing on his approval score, presidency experts say.
But they do indicate a margin of maneuver for Reagan that can help reverse the negative slide recorded recently in many surveys.
The poll data shows a heavily critical view of Reagan's performance less than 1 1/2 years into his first term. ''Only four in 10 now express confidence in 'Reaganomics,' '' the Gallup Poll headlines a survey. ''Public leans to view that Reagan should not run in '84.''
Pollsters asking different questions about presidential performance trace a similar trend. The Harris survey in April found only 38 percent rated ''the job Reagan is doing as president excellent or good,'' 61 percent fair or poor. This was three points more negative than in March and a reversal from a positive January rating -- 52 percent excellent or good, 47 percent fair or poor.
Gallup's latest poll, which asks whether the public ''approves'' or ''disapproves'' of a president's performance, was marginally negative -- 45 percent approve, 46 percent disapprove, or about the same as in March. The ABC News-Washington Post poll showed a similar holding steady in recent weeks, but at a more positive level for Reagan -- 51 percent approve, 44 percent disapprove.
The Roper Organization, which asks yet another question -- whether Americans are ''supporters'' or ''critics'' of the President - found Reagan's standing had exactly reversed from last December to March, from an eight-point positive rating (54 percent supporters, 46 percent critics), to an eight-point negative rating.
By Roper's tracking, Reagan reached a negative rating 15 months earlier than did Jimmy Carter during his term. At the same point in the Carter presidency, early spring of the second year, Mr. Carter scored 53 percent positive, 40 percent negative.
Presidents do come back from popularity recessions. Carter plunged to a 35 percent positive-59 percent negative Roper rating in July 1979, the time of his retreat to Camp David. He revived to a 48-47 positive rating in May 1980 during the presidential primaries, then sank negative again (35-57) in July, just prior to the Democratic convention.
''I wouldn't be surprised if Reagan's negative public voting leveled off or came back a little,'' says Burns W. Roper, president of the Roper Organization. ''The economic recovery would definitely help him.
''The Falklands will help him, too. We're on Britain's side. This is seen in a context of assertiveness for the free world. Britain is sort of an extension of us. This is rising up and taking action instead of being pushed around.
''While attention is heavily on jobs and deficits, the inflation rate is coming down, and that should help him, too.''
The budget drama in coming weeks holds potential pitfalls for Reagan, and for his party in the fall elections, GOP strategists say.
''The current recession is clearly laid by the public on Carter and the Democrats of the last 20 years, by a margin of 3 to 1,'' says one Republican official in charge of his party's fall campaigns.
''But the driving force behind that is the perception that Reagan has done something - that he's in control. That perception can be messed up by a clash between Congress and an inflexible president. In that case, the Republicans become the agent of economic negativism. We have less than a month. If we don't see positive, coordinated action by the Republicans, a semblance of Republican unity on the budget, it will become our recession. We can't afford that in an election year.''
The Democrats see Reagan as having gained somewhat in last week's showdown with Democratic leaders over the budget. But they see him as weaker than he was, and longer-range trends working in their favor.
''The President came out ahead, but nowhere the way he was ahead in previous encounters,'' said a spokesman for the Democratic leadership.