When it was introduced early this year, the Reagan administration's plan to nurture economic growth in the Caribbean through trade benefits enjoyed an almost euphoric reception on Capitol Hill.

But in the harsh realities of the House Ways and Means Committee these days, the glow is fading. Selected American industries are howling for relief, organized labor is unhappy and some congressmen are threatening to fight it to the bitter end.

The conflict over the Caribbean Basin Initiative reflects the difficulty of passing any legislation to help even a poor country's primitive industries at a time of high unemployment and recession in the United States. Jobs gained in the Caribbean will mean jobs lost in the United States, critics argue.

And the Ways and Means subcommittee on trade yesterday punched a couple of holes in the Basin concept of permitting exports to the United States from selected countries in the Caribbean. By a close vote, it exempted the leather and rubber footwear industries from the duty-free privilege in a move to protect American manufacturers from competition.

It also slapped a tariff rate quota on rum imports from Caribbean countries, a move designed to protect the rum industries of the Virgin Islands and Puerto Rico.

As the subcommittee adjourned, it also was considering an amendment protecting American perishable farm products from potential injury by Caribbean products.

The debate on exemptions prompted a sharp exchange between the administration's chief supporter, Rep. Sam M. Gibbons (D-Fla.), the chairman, and the most vocal opponent, Rep. Don Bailey (D-Pa.).

Gibbons noted the United States already runs a $3.4 billlion trade surplus with the mostly poor Caribbean nations that the plan would help. "If they can't sell us something, we are going to have to subsidize them for the rest of our lives," he said. "They don't have any credit or any money or any jobs."

Bailey claimed the basin plan's duty-free concept would cost American jobs and would not uplift Caribbean economies. "It doesn't make any sense to parcel out 50-cent-an-hour jobs down there," Bailey said. "It's not going to teach the people how to do anything."

The administration strongly opposed each proposed exemption yesterday. The subcommittee voted against exemptions for tuna, rum, automobile parts and mushrooms.

President Reagan proposed the initiative to give tariff preferences, economic assistance and investment incentives to a region of generally poor countries. He's asking $350 million in economic aid this year, a proposal generally well-received although criticized by some as insufficient.

The trade segment of the package, however, has aroused well dug-in opposition from certain industries and labor groups that predict it will siphon off jobs and production. The administration already has sought to lessen the opposition by excluding textiles and guaranteeing relief for American sugar producers from foreign suppliers.

So far, the administration has dug in its heels to stem the flow of exceptions to the duty-free benefits. "Exemptions beget exemptions," said Stephen L. Lande, assistant U.S. trade representative.

Progress has been slow to date in the committee. Two scheduled mark-up sessions passed without action on any of the more controversial amendments introduced by Bailey and others. Behind the scenes, the administration was working to soften the opposition.

Gibbons, the most determined supporter of Reagan's plan, speaks with considerable passion about the need to extend a friendly trade hand to Caribbean nations.

"There is a tremendous need for help in that part of the world," Gibbons said. "They've suffered the run-up in oil prices.

"Many have lost their old markets. Commodity prices are down. Sugar, coffee prices are down. There is a steadily deteriorating position."

Gibbons disputes the claims that American employment will be adversely affected. "I don't think this would take away U.S. jobs," he said.

"These countries import far more from us than we buy from them. Twenty out of the 23 countries have a trade deficit now with us."

His arguments do not dim the opposition of subcommittee members such as Bailey, who claim that the bill offers overly generous inducements to manufacturers to base their operations in Caribbean countries and then compete with U.S. producers.

Bailey observes that the bill would extend duty-free benefits to any product for which the value of the local production amounts to at least 25 percent of the value of the whole.

The usual requirement under trade rules for developing countries is 35 percent.

Bailey said that provision could induce third countries to ship products through a Caribbean country, perform a modest amount of local production, and then export them duty-free