As Congress and the administration agonize over budget cuts, tax hikes and other weighty matters, there is still the unresolved problem of Marvin C. Westcott's leopard skin.

Westcott's leopard skin sits tanned but unmounted in England, awaiting passage of a bill that would lift a corner of the Endangered Species Act just enough to let it slip into the United States.

Meanwhile, there are sheepherders in western Texas who could use a little help from Uncle Sam in coping with foreign competition. Draper-King Cole Inc. wants to save a little money importing carrots, and the Stitt Spark Plug Co., a small firm in Conroe, Tex., locked in a competitive struggle with Champion Spark Plug Co., wants to reduce the cost of certain ceramic insulators.

All these individuals and companies, along with a host of others, have gone to their friendly congressman or senator to get some relief. What they want, in most cases, is a reduction in the import duty on foreign goods they use in manufacturing, although in some cases, like the Texas lambs, they want higher import fees to protect a domestic industry. It helps if the legislator serves on either the House Ways and Means or Senate Finance committees.

In the House, the relief--one of the few methods of distributing patronage still available to members of Congress--has emerged as HR 4566, umbrella legislation combining "17 noncontroversial tariff and trade bills," according to the committee report. The measure passed the House without objection Oct. 13 under suspension of the rules and now awaits consideration by the Senate Finance Committee.

The Finance Committee, in turn, has issued a request for public comment on 13 pending tariff bills on subjects ranging from carrots to fishnets to potatoes.

Although all the beneficiaries of the bills feel deeply justified in their requests for congressional relief, the scope of the public interest in the bills varies widely.

A bill sponsored by Sen. Edward Zorinsky (D-Neb.), for example, reads in its entirety:

"Be it enacted by the Senate and the House of Representatives of the United States of America in Congress assembled that, not withstanding any other provision of law, Marvin C. Westcott of Holdrege, Neb., is authorized to import in the United States, for noncommercial purposes only, one leopard (Panthera pardus) skin trophy."

Westcott, in a telephone interview, said he shot the animal in Kenya in 1975 under the mistaken impression that the Endangered Species Act would soon be amended to exempt leopards. They "are one hell of a long way from endangered," said Westcott, a veteran of a number of African shooting trips. He said he was somewhat reluctant to discuss the bill because of adverse press reports that had appeared in some Nebraska papers.

The Zorinsky bill is unusual in that it is directed to an individual, and it seeks exemption from the Endangered Apecies Act, not the raising or lowering of a tariff. Most of the bills are aimed to benefit one or a small group of companies, almost invariably in the sponsor's district or state.

One bill, which has been privately dubbed "Kemp-Roth II" after the sponsors of the across-the-board individual tax rate cut, Sen. William V. Roth (R-Del.) and Rep. Jack Kemp (R-N.Y.), would temporarily suspend the duty on bulk carrots used primarily by canners. An aide to Roth noted that the legislation is of some importance to Draper-King Cole Inc., a carrot canner in Milton, Del., while a Kemp aide pointed out that the J. C. Brock Co. near the congressman's Buffalo, N.Y., district imports carrots.

In another case, a section in the House bill lowering the duty on "ceramic insulators to be used in the production of spark plugs for natural gas-fueled, stationary, internal combusion engines" could well determine the ability of a tiny Conroe, Tex., firm to compete in a highly specialized market against the giant in the spark plug industry, Champion.

Stitt Spark Plug Co., a firm employing 52 persons, must import ceramic insulators to use in the manufacture of spark plugs at a 12.8 percent duty rate, when the duty on completed spark plugs is only 3.8 percent. The firm has, to date, been able to win its case with Rep. Charles Wilson (D-Tex.), whose district includes Conroe, the sponsor of the legislation, and the Ways and Means Committee, which included it in the omnibus bill.

Or take the case of Treasure Masters, a small firm in Dairy, N.H. It makes sachet bags, small cloth bags that are perfumed and kept by women in their lingerie drawers. Treasure Masters, however, imports a small piece of embroidery from Switzerland to make the sachet bags more attractive, and has persuaded Sen. Gordon Humphrey (R-N.H.) to sponsor legislation to lower the duty on "sachet parts of cotton or man-made fibers, embroidered."