President Reagan, trying to drum up support for a $100 million aid package for the Nicaraguan rebels, met yesterday with three rebel leaders and warned that the United States faces a "strategic disaster" of great magnitude and a "vast migration" of refugees if Congress turns down his request.

"Defeat for the contras would mean a second Cuba on the mainland of North America," Reagan said at the White House meeting. "It would be a major defeat in the quest for democracy in our hemisphere. And it would mean consolidation of a privileged sanctuary for terrorists and subversives just two days' driving time from Harlingen, Tex.," a city near the Mexican border.

With the leaders of the United Nicaraguan Opposition at his side, the president warned that "congressional defeat of this aid proposal could well deliver Nicaragua permanently to the communist bloc."

Meanwhile, Secretary of State George P. Shultz added a new note in the administration's campaign for aid to the contras, warning that the alternative is "a vision of two, three, many Nicaraguas -- a hemisphere of burning churches, suppressed newspapers and crushed opposition."

State Department officials said the "burning churches" statement apparently referred to the burning of Miskito Indian villages in 1981-82 by Sandinista forces in an effort to force the inhabitants out of a contested coastal area.

Despite the intensity of the rhetoric from Reagan and Shultz, administration political strategists acknowledge that the odds are against them in their efforts to win the $70 million in military aid that the president said is an essential part of the package. Prospects are considered brighter for the $30 million in humanitarian aid.

On Capitol Hill, Senate Assistant Majority Leader Alan K. Simpson (R-Wyo.) said there is a "good prospect" for the aid package if Reagan goes all out for it with a nationally televised speech, which his aides have said is likely.

But Rep. Dave McCurdy (D-Okla.), considered a key swing vote, announced that he will oppose the package and said he is "fairly confident" that 30 other congressmen who supported last year's decision to grant $27 million in humanitarian aid will agree with him. He expressed anger at both the administration and House Democratic leaders for demanding a quick vote "for political reasons, while there are those of us in the middle who are concerned about policy."

Another swing voter, Rep. Charles E. Bennett (D-Fla.), said he will support the aid request and was reassured by Reagan's pledge not to use U.S. troops in Nicaragua and his reaffirmation of U.S. treaty commitments.

Votes are now expected in both houses of Congress during the third week of March. A senior White House official said yesterday that "this gives us less time than we may need to build the pressure," particularly in the House.

McCurdy said he has been working on a compromise proposal with Senate leaders that would call for renewed diplomatic efforts and a restructuring of contra leadership to broaden and democratize it. And Sen. Jim Sasser (D-Tenn.) proposed putting the aid in escrow for six months while the United States negotiates with Nicaragua toward a peace settlement, a position the administration has rejected in the past.

The president and the rebel leaders insisted that they have actively sought a diplomatic solution but that the Sandinistas aren't interested.

"We want a real two-track approach that will seek a political solution," said Alfonzo Robelo, one of the three rebel leaders who met with Reagan. "But the Sandinistas will never look into the political situation seriously unless they have the pressure."

Reagan said that a Sandinista victory over the contras would enable them to turn their attention to overthrowing neighboring democracies.

"I think it would place in jeopardy the survival of each of those small and fragile democracies now in Central America, open up the possibility of Soviet military bases on America's doorstep, could threaten the security of the Panama Canal [and] inaugurate a vast migration northward to the United States of hundreds of thousands of refugees," the president said. "And those who would invite this strategic disaster . . . will be held fully accountable by history."

The Nicaraguan government responded to the White House meeting and Shultz's speech by saying those actions were "additional proof" of the administration's "commitment to a military solution in Central America."