President Reagan yesterday asked Congress to give the Nicaraguan contra rebels $36.2 million in lethal and nonlethal aid, while House Democratic leaders said they were preparing a counterplan, limited to humanitarian assistance.

The Democrats said they likely would offer their plan if the administration package is defeated.

The Democrats put no price tag on their proposal, which White House aides described as a tactic designed to head off growing support among swing voters for the administration plan, which faces a showdown vote next Wednesday in the House.

"We think once the Feb. 3 vote is over, we will put something bipartisan together," said Rep. Tony Coelho (D-Calif.), the House majority whip. "Feb. 3 is a new beginning for us. We don't intend to turn our backs and run away."

Will Ball III, the chief White House lobbyist, said that "we have a fighting chance to win" the House vote on the president's scaled-down proposal. Reagan is scheduled to make a nationally televised appeal speech in its behalf next Tuesday.

Reagan unveiled his latest contra aid proposal in a speech to an audience of reserve officers who cheered when he declared, "I didn't come to Washington to preside over the communization of Central America." The president said rejection of the aid request would have the "catastrophic consequences" of assuring continuation of "a Marxist-Leninist regime on the American mainland."

Only 10 percent of the package -- $3.6 million -- would be for military assistance and this would be held in a separate account until March 31. If the Sandinista government in Nicaragua and the contras fail to reach a cease-fire agreement by then, Reagan would be free to release the military aid. But he promised to consult the leaders of Costa Rica, Honduras, El Salvador and Guatemala before doing so.

The remainder of the assistance would be for nonlethal aid, such as food, supplies and clothing. But it also would include such items as helicopters and jeeps, which can be used in combat. Not included in the proposal was $20 million that would ensure replacements for any planes that are lost taking supplies to the contras. One such plane was shot down last weekend.

The Democratic alternative, on which there is no firm price tag, is being developed by the party's leadership in an attempt to give swing Democratic voters a choice between cutting off all contra aid and accepting the administration proposal. The leadership alternative could include general economic and trade assistance to other Central American nations and is tied to continued progress in the peace process. The humanitarian aid would be delivered by an international organization such as the Red Cross or the Organization of American States.

Despite Reagan's strong words on behalf of the contras, whom he credited with wresting limited democratic concessions from the Sandinistas, the Reagan aid package was far below the level of contra aid the president has sought in the past.

Last fall the administration wanted a $270 million package to fund the contras for an 18-month period that would have extended into the next presidency. A month ago, officials were talking about $100 million in aid for a six-month period. Last week that amount shrank to about $50 million.

It is unclear how long the most recent request covers, but it gives the administration the right to make a new request in July.

Yesterday's events came as supporters and opponents of further military aid to the Nicaraguan rebels scrambled during a series of public and private meetings to win the support of the 20 to 30 House members of both parties whose votes are considered crucial to determining the outcome of next Wednesday's vote.

The White House invited both Democratic and Republican House members to private meetings with Reagan. The president met with House Speaker Jim Wright (D-Tex.). Contra aid supporters brought Nicaraguan government defector Major Roger Miranda Bengoechea to Capitol Hill. And contra assistance opponents unveiled a television ad campaign to run in the home districts of key members.

The leadership's concessions to a group of moderate Democrats led by Rep. Dave McCurdy (D-Okla.) may turn out to be pivotal. In agreeing to support a package of purely humanitarian assistance if the administration aid request is defeated, the leadership appears to have won the support of many of the moderates who supported McCurdy's effort late last week to delay Wednesday's showdown vote. Many of the 20 or so Democrats who joined with McCurdy oppose military aid but want to keep pressure on the Sandinista government to continue its apparent commitment to the Central American peace process.

"We feel we have to be for something and not merely against the administration plan," said Rep. Thomas R. Carper (D-Del.), a member of the swing group who said yesterday he would vote against the president's request if given a chance to vote on a humanitarian assistance alternative.

"To the extent we have that promise, to the extent the administration package has lethal aid with a presidential trigger, that brings the lion's share of the moderates" behind the leadership alternative, Carper said.

Carper has proposed that the alternative package include about $10 million in humanitarian aid over three months, that it be delivered by the CIA network with provisions for an independent inspection, and that it be linked to the beginning of multilateral peace talks between the United States and the five Central American nations.

Nicaraguan Ambassador Carlos Tunnermann said yesterday that "If the request is approved, the zealots within the administration will have succeeded in killing the {Costa Rican President Oscar} Arias peace plan," saying all five Central American presidents oppose further contra funding.

Wright said he told the president yesterday that "I thought it {the administration request} would probably be rejected if there is any significant military money in it and, in my opinion, it is more likely to gain approval if there is only humanitarian aid."

House Republicans, however, still held out hope that Reagan's modest request for military aid could pass.