The White House has launched a coordinated government public relations campaign to persuade special-interest groups and other Americans that President Reagan's efforts to counter communism in Central America are vital to U.S. security.

"The judgment of history on this president will probably be based on what happens in Central America," said Faith Ryan Whittlesey, director of the White House office of public liaison, whose Central American Policy Outreach Group is coordinating the campaign. She argued that the United States faces "the Eastern Europeanization of its southern border" and the prospect of Soviet-backed regimes throughout the region.

"Every businessman who asks me about natural gas or consumer product safety, I ask to help us on Central America," Whittlesey said. "The president has made a commitment, and we intend to follow through and mobilize public opinion."

She said anti-communist appeals are being made to ethnic groups, and Jewish organizations are being told that forces most hostile to Israel--including the Palestine Liberation Organization, Libya and Eastern European nations--are supporting leftists in Central America.

Whittlesey's group meets each Monday with mid-level government officials involved in Central America policy development and each Wednesday with other administration officials and invited representatives of special-interest groups. Administration officials are urged to sell Reagan's Central America policy in all speeches and public appearances, regardless of the audience or primary subject matter.

The groups have been lectured on the rationale of Reagan's policy of increasing military aid to friendly forces in Central America by White House national security affairs adviser William P. Clark, presidential counselor Edwin Meese III and specialists from the State and Defense departments.

Two members of the U.S.-supported guerrillas fighting the leftist Sandinista government in Nicaragua also spoke at one meeting, denouncing the Sandinistas for "betraying the revolution" and talking optimistically about the anti-Sandinista military movement.

According to White House officials, the group has decided on these basic arguments for strong U.S. action to stop the spread of communist influence in Central America:

* The region is vital to U.S. security because of its proximity and because other nations in the region would be threatened if leftist guerrillas overthrew the U.S.-backed government in El Salvador. "If El Salvador falls, Honduras and Costa Rica wouldn't be far behind," said former Republican congressman John H. Rousselot, White House liaison with the business community.

"The national security of all Americans is at stake in Central America," says the White House Digest, a new publication to be distributed to voter groups. "If we cannot defend ourselves there, we cannot expect to prevail elsewhere. Our credibility would collapse, our alliances would crumble, and the safety of our homeland would be put in jeopardy."

* What happens in Central America is also vital to the U.S. economy, because considerable U.S. shipping passes through the Caribbean, and American businessmen have interests in the region that could be jeopardized. "How many Hershey bars do U.S. businessmen sell in Cuba?" asked Rousselot rhetorically.

* There also are "moral and humanitarian issues at stake in Central America," according to Whittlesey, who talked of the potential of 10 million refugees fleeing here from Central America if communist influence spreads.

Administration officials have emphasized this specter of a flood of refugees. Reagan asked in his April 27 speech to Congress: "Must we wait while Central Americans are driven from their homes like the more than a million who have sought refuge out of Afghanistan, or the 1 1/2 million who have fled Indochina, or the more than a million Cubans who have fled Castro's Cuban utopia . . . ?"

Whittlesey acknowledged that public opinion polls, including those made for the White House, show widespread public opposition to Reagan's policies in Central America. But, adding that the polls also show "most Americans don't know where El Salvador is, let alone the policy implications of what we're doing," she contended that public opinion can be changed.

"As a politician, I like to turn political minuses into political pluses," she said. "I believe that, when people understand what the stakes for the United States are in Central America, this issue has the potential of becoming a political plus for the administration."

Not everyone in the Reagan administration agrees with this, however. "We risk the danger that we're going to be sending the wrong signal," said one official. "We risk making people fearful of U.S. troop involvement when there is no grounds for fear."

Whittlesey responded that ignoring the issue at the White House level would risk making Central America "seem less important than it is" and undermine the president's policy.