President Reagan has no problem with Congress in regard to Nicaragua. He can doubtless bully the legislators into voting military aid for the contras, especially now that he says he has found himself some Cubans in combat.

No, his problem is with the United States, the hemisphere and the world, none of which stands with him in his obsession to overthrow the Sandinista government.

His muscular and violent Central American policy is a hit on the right-wing banquet circuit, where calls for supporting the contras, or counterrevolutionaries, draw stormy applause; elsewhere, such a call gets boos or yawns.

Every day, more U.S. churches offer sanctuary to Central American refugees. Several American cities -- most lately, Los Angeles -- have proclaimed their intention to resist the deportation of political fugitives.

Recently, Bishop Thomas J. Gumbleton of Detroit came to town as the leader of an ecumenical organization called Quest for Peace, which has vowed to raise $27 million for the people of Nicaragua to counter the $27 million that the House meekly voted for the contras in June. The bishop announced cheerfully at a press conference attended by representatives of Protestant and Jewish groups that it was his hope "to reverse the policies of the administration." Already, $9 million has been collected.

The resistance of the Catholic hierarchy to Reagan's cloak-and-dagger moves in Central America is a particular cross for the president to bear. He constantly reminds the clerics that the Nicaraguans heckled the pope during his visit to Managua, that the Sandinista government is restricting the movements of its most vociferous clerical critic, Cardinal Miguel Obando y Bravo. Yet they declare at every opportunity that no military aid should be sent to the area.

The rest of the world understands no better. Not a single country, not even El Salvador, has joined the embargo Reagan imposed on Nicaragua in May.

In his melodramatic Saturday radio speech, the president once again wrapped himself in the mantle of defender of the church: "No institution more deeply embodies or glorifies or seeks to perfect the moral and spiritual goodness" of man, "yet in Nicaragua, the church is the enemy."

Nobody seems to be listening -- except, of course, Congress, which has received yuletide notice that Reagan is going to make support of the contras a campaign issue, and redbait those who do not go along.

The Cuban charge was aired by Elliott Abrams, assistant secretary of state for inter-American affairs, who has won favor with his superiors for representing things in El Salvador as better than they are and in Nicaragua as worse. Like the administration's previous charge of massive shipments of arms from Nicaragua to El Salvador, the Cuban charge is undocumented.

But the mention of Cubans anywhere makes congressional blood run cold. The presence of Fidel Castro's men in Angola is being used to drum up a rerun of our disastrous intervention there.

Reagan said -- and he was talking to cringing members of Congress, not the country -- "If Nicaragua can get material support from communist states and terrorist regimes and prop up a hated communist dictatorship, should not the forces fighting for liberation now numbering over 20,000 be entitled to more effective help?"

His hemispheric rationale for keeping the contras in the ring is unraveling. Supposedly the reason for soldiering on is our responsibility to Nicaragua's neighbors, who are, it is said, privately cheering us on.

Their actions are speaking somewhat louder. Honduras is stubbornly refusing to move to the contras the $27 million in "humanitarian" aid approved by Congress in June. The president sent his new National Security Council adviser, John M. Poindexter, to the area last week to straighten them out.

But while Poindexter was lecturing the Hondurans, the newly elected president of Guatemala, Vinicio Cerezo, was calling on his neighbor, the "dictator in designer glasses," as Reagan called Nicaraguan President Daniel Ortega.

Cerezo called on other neighbors, too. The significance of his stop in Managua is that he is not about to treat Ortega like a terrorist pariah. Administration officials are miffed at Cerezo and growl about cutting U.S. military aid to Guatemala.

When he was clubbing the House into voting $27 million for the contras, Reagan promised to talk to the Sandinistas. He never has. His message to Congress is that real men don't negotiate, and only wimps seek regional solutions.