Amid signs that the political strength that made him Western Europe's pivotal leader is ebbing, West German Chancellor Helmut Schmidt will try to dispel concerns about his leadership when he visits Washington this week for talks with President Reagan.

Illustrating Schmidt's recent political problems, West Germany's largest-circulation magazine last week carried a cover photo of the chancellor sporting a swollen black eye.

On top of the bruise, which had been sketched in, was a Star of David, intended to represent the public abuse the West German leader suffered recently from Israeli Prime Minister Menachem Begin after Schmidt's trip to Saudi Arabia and his statement that Palestinians have a moral right to self-determination.

The Begin punch was generally regarded here as undeserved. But the Israeli symbol in the picture could easily have been substituted by a number of other signs depicting the problems pulling Schmidt down in the popularity polls -- a nuclear missile, a shrunken West German mark, an unemployed worker, an unfinished atomic power plant, a reproachful young protester.

Half a year after winning reelection in a national campaign that touted the confident Schmidt as Europe's expert crisis manager, the West German leader has slipped to an all-time low in national popularity polls.

In one early spring survey, 60 percent judged his government's performance negatively. According to another poll, Schmidt's own approval rating, which in the past had buoyed his less-popular Social Democratic Party, dropped steeply since lasy year to 41.5 percent. That pollster noted that public regard for Schmidt's government is lower now than it was for Willy Brandt's government before Brandt quit in 1974 and allowed Schmidt to succeed him.

During an interview with American correspondents Friday, Schmidt, 62, sought to give the impression that he had things under control. Asked how he would answer U.S. worries about his political troubles, Schmidt replied in English, "It lies in the nature of difficulties that are being overcome."

He appeared relaxed and looked fit following reports that he was ill during the winter. Having seemed for a time to by lying low amid a swirl of political challenges, he has come forward since early April firing rounds of verbal volleys in interviews and speeches, may directed at critics of Atlantic Alliance plans to station new medium-range nuclear missiles in Europe.

But the pressure of Schmidt is not something that can be debated away easily. It stems from factors outside his country -- from the Soviet invasion of Afghanistan and the upheaval in Poland that crimped his government's active detente policy, and from higher oil prices and Japanese competition that caused the West German economy to stagnate, ballooned the country's balance of payments and undercut the mark.

Among West German political groups, these developments cut most deeply at the policies and dreams of Schmidt's own Social Democratic Party, which championed detente and expanded expensive social programs during its decade as senior partner in the Bonn coalition.

The party's malaise was deepened further this spring by election losses, most significantly in West Berlin where the party's nearly uninterrupted postwar rule was ended.

The chancellor's friends believe that much of the frustration in the party ends up directed personally at Schmidt, who has tended to be held in suspicion particularly by the Social Democratic left for being too pragmatic.

Of top concer at the moment for Schmidt and his party is the NATO missiles plan, which Schmidt agrees is essential to achieve a balance of power in Europe but which makes his party nervous because it goes against its traditional disarmament plank.

Two weeks ago a regional Social Democratic Party congress in Baden-Wuerttemberg called for a review of the NATO decision at next year's national party convention. The call reflected concern about U.S. foot-dragging on arms control negotiations with the Soviet Union that were to follow the missiles decision.

Any action by the party to qualify its support for the NATO plan would be grounds for the government's junior coalition partner, the Free Democrats, to switch allegiance and form a new government with the Christian Democrats, throwing the Social Democrats into opposition. Some Social Democrats, in fact, have said that a return to the opposition might not be a bad thing for regenerating the party.

In view of the personal political stakes involved, and the threat posed to NATO solidarity should the Bonn government appear to waver on the missiles plan, Schmidt seems to have taken a sharper tone recently in public statements on the Soviet threat to the West.

Schmidt said in Friday's interview that he was not aware of using harsher language about the Soviets, adding that he did not like to use harsh language in public out of in consideration for diplomatic relations.

The tougher language has been carefully threaded through his old theme of the need to cooperate with the Soviets, allowing a listener to choose the words he wants to hear. But the chancellor's aides have tended to emphasize recently, at least to U.S. correspondents, the critical talk about Soviet behavior.

Schmidt's basic policy position toward the Soviet Union does not seem to have changed. He continues to stress the double track of detente and military balance, though appreciating that the possibility of pursuing the detente track at the moment is restricted.

Schmidt said he was convinced that his party would continue to support the NATO missiles decision, despite the Baden-Wuerttemberg action, which he dismissed as a regional trend.

"What counts are the votes in parliament, sir," he quipped when asked about it.

Several times he said that debate about security policy, particularly among the young, should be expected in a country with a military draft. He recalled that the United States had done away with its draft "in order to get rid of a great deal of trouble with the younger generation."

As a result, Schmidt said, "we are asking more from [the younger generation] presently than you do from yours. So necessarily our difficulties with our students must be a little higher than yours."

With his room for political maneuver sharply narrowed in the fields of economics and foreign policy, Schmidt has appeared to plot his moves more cautiously and to sound at times a bit defensive. In a lecture in March on "Kant in Our Time," he spoke of the duties and responsibilities of a politician, a theme he has repeated since.

As a West German journalist observed at the time, "It was almost a plea for understanding for the difficulties politicians have in reaching a decision and explaining themselves."

Schmidt is unlikely to find an easy formula to resolve West Germany's new frustrations. But he can be expected to try especially hard now for good relations with the United States, after four years of maintaining a certain distance from the Carter administration.

This has become a necessity since the defeat of French President Valery Giscard d'Estaing, a close friend of Schmidt's and formerly a key to Bonn's efforts to develop economic and foreign policies that could shield Western Europe from U.S. shocks.

Schmidt needs two things from the Reagan administration. One is a convincing commitment not just to restart talks with Moscow on nuclear weapons in Europe -- a promise already made -- but also indications that broader talks on U.S.-Soviet strategic arms will be resumed. The second is relaxation of high U.S. interest rates, which have served to draw funds from Europe, contributing to the weakening of the West German mark.

On the second topic, Schmidt sounded hopeful that some sort of understanding could be reached among the heads of the seven leading Western industrialized nations at the Ottawa summit meeting in July.