President Reagan's policy in Central America suffered another setback yesterday when House Republicans failed in an effort to force a new vote on May 12 on military aid to the Nicaraguan rebels.

As a result, the House is unlikely to vote on the aid issue until mid-June, and some Republicans acknowledged yesterday that the president may never get the military aid package he wants. If the House does vote some kind of aid package in June, it could falter in negotiations with the Senate.

The Reagan administration has said repeatedly that the counterrevolutionary rebels, known as contras, are in danger of being crushed by Nicaragua's Sandinista government unless they receive an immediate infusion of U.S. assistance.

House Republicans had hoped to gather 218 signatures -- a majority of the House -- on a "discharge petition" that would have forced the contra aid issue back to the House floor on May 12, the earliest possible date under the discharge petition procedure. They had until yesterday to achieve this for the May 12 target date, but fell short.

The Republicans obtained only 159 signatures of the 218 they needed, including the signatures of seven Democrats. There are 182 Republicans in the House.

Under House rules, legislation that is the subject of a discharge petition can be brought to the floor only on the second and fourth Mondays of the month. The next possible date, May 26, is Memorial Day, when Congress will be in recess, meaning the issue is likely to be put off until June 9 at the earliest.

Earlier yesterday, the House Democratic leadership moved to preempt the Republican discharge petition strategy by promising leaders of a group of moderate Democrats a chance to attach a contra aid package to the military construction appropriations bill that is scheduled to be considered by the House the week of June 9. House Majority Whip Thomas S. Foley (D-Wash.) said the "overwhelming majority" of moderate Democrats were satisfied with this pledge and would not sign the discharge petition.

Foley made this promise yesterday to Rep. Dave McCurdy (D-Okla.), the sponsor of an amendment that would place restrictions on Reagan's request for $70 million in military aid and $30 million in nonlethal assistance to the contras.

The House first rejected the president's request on March 20. The Senate then passed a slightly modified version of the aid package, which was returned to the House floor on April 16. However, House Republicans, fearing that the restrictions proposed by McCurdy would be adopted, prevented a second vote on the issue, opting instead to begin the discharge petition for what they called "a clean shot" on the Reagan proposal.

GOP leaders are maneuvering for House approval of the Senate-passed aid package, which would then go immediately to the president for his signature. They want to avoid returning the aid measure to the Senate, where it faces a possible filibuster and could become bogged down amid legislative battles over the budget.

Such a scenerio appears likely if the McCurdy version of the proposed aid package is attached to the military construction appropriations bill in June.

Discouraged Republicans said that if they failed to meet the May 12 target date they would have to reassess their strategy, perhaps trying other methods to force a new vote before June.

"I think the Democratic leadership's wish [to block any contra aid package] could become a reality," said one GOP leadership aide.