Chancellor Helmut Kohl, whose prestige has been damaged by a string of setbacks in recent weeks, is encountering a rising tide of dissent from fellow Christian Democrats who are worried that his troubled stewardship could hurt the party's chances to remain in power after the 1987 elections.

During his 2 1/2 years as chancellor, Kohl has displayed an uncanny knack to ride out controversies and emerge from political embarrassments without endangering his stature as party leader.

But last Sunday's overwhelming defeat in a key state election in North Rhine Westphalia, following the controversy over President Reagan's visit to West Germany and the meager results of the seven-nation Bonn economic summit, has intensified debate among Christian Democrats over whether Kohl is becoming a serious political liability.

In an emotional parliamentary debate last Tuesday, Kohl looked ill at ease and on the defensive as he tried to answer opposition charges that his handling of Reagan's trip to the Bitburg military cemetery and the economic summit had eroded West Germany's relations with the country's principal partners, the United States and France.

The French blocked the setting of a date for international trade talks, a U.S. priority, and announced their rejection of the U.S. invitation to join in research for the "Star Wars" antimissile defense.

Christian Democrats have been traditionally fickle with their leaders, especially those who failed to win elections. Ludwig Erhard, the architect of the country's postwar economic recovery, was replaced as chancellor by the party four months after it lost an election in North Rhine Westphalia in 1966.

Last Sunday's balloting in the same state, where one-third of all West German voters live, gave Kohl's party less than 37 percent of the vote, even worse than its loss under Erhard.

Uwe Barschel, a leading Christian Democrat who serves as state premier in Schleswig Holstein, noted that in the past year the party has grown increasingly divided over its economic and security policies. "Kohl and his government must share the guilt for the party's bad results," he said.

The anxiety among Christian Democrats looking toward the 1987 elections is spreading because the center-right coalition has failed to reduce the country's high unemployment rate, which voters have cited as the dominant issue in recent state elections.

In addition, the opposition Social Democrats now appear to be rallying around a popular moderate, Johannes Rau, as their likely candidate to run for chancellor in the March 1987 elections.

Rau, a charismatic politician and eloquent speaker, carried the party to victory as premier of North Rhine Westphalia, easily outpolling his stodgy Christian Democratic rival, Bernhard Worms, who was Kohl's personal choice.

Christian Democratic strategists fear that Rau could run a much stronger campaign against Kohl than Hans-Jochen Vogel, the lackluster floor leader of the Social Democrats who lost to Kohl in 1983, or the left-wing Saarland premier, Oskar Lafontaine, whose anti-NATO and antinuclear views appeal to young voters but antagonize the moderate majority.

Despite the growing concern about the shape of the next election, Christian Democratic rebels have been unable to find an alternative candidate who could build momentum behind a "dump Kohl" movement.

The pro-government Frankfurter Allgemeine newspaper observed in an editorial that while "doubts in the party are growing about Kohl," he probably will not be replaced because of the flaws of his potential challengers.

Finance Minister Gerhard Stoltenberg is disliked by party leaders; Bavarian Premier Franz Josef Strauss is getting too old, and popular Baden Wuertemberg Premier Lothar Spaeth is still considered too inexperienced.

Moreover, Kohl would undoubtedly wage a bitter struggle to maintain power, and the spectacle of a polarizing leadership fight could inflict incalculable harm to the party's standing before the election.

While Kohl has gained a reputation as an accident-prone government leader and a bumbling statesman, his sheer endurance and innate understanding of basic German yearnings remain unquestioned political assets.

Unlike Erhard, who was primarily an economist and technocrat, Kohl is recognized as a shrewd grass-roots politician who has accumulated debts of loyalty from many provincial Christian Democrats. Since becoming party leader in 1973, Kohl has more than doubled party membership and built up a populist base including support from churches, trade unions and industry.

At a post-election review, Kohl admitted to leading Christian Democrats that he had suffered "a grave personal defeat" in Sunday's vote. He vowed to tackle the two key issues the Social Democrats exploited: unemployment and proposed cuts in pensioners' benefits.

Kohl's government has planned a two-stage tax cut, in 1986 and 1988. But some coalition members are insisting that the tax cut package should be moved up to bolster the economy in time for the election.

There is also strong speculation that Kohl may shake up his Cabinet soon to get rid of some officials who have performed poorly or caused political problems. Defense Minister Manfred Woerner and Agriculture Minister Ignaz Kiechle are cited as two possible candidates for firing.