WHEN Dominick Spadea began manufacturing submachine guns at his tool-and-die shop in this Camden County community in 1982, he had no idea that he soon would be, as he put it, ''stepping on the tail of a dinosaur'' - the State Department.

The department denied Mr. Spadea's request for an export license for the guns last August. He had been offered a $5 million contract by Afghan rebels who have been fighting Soviet troops in their country since 1979. The rebels, Mr. Spadea said, ordered 10,000 weapons.

Although the rebels have been receiving covert military aid from the United States - estimated at $200 million over the last two years - Mr. Spadea's venture would represent overt and private aid.

Senator Frank R. Lautenberg, Democrat of Montclair, declined to help Mr. Spadea pursue his request for an export license, but Representative Jack Kemp, the New York Republican and widely considered a potential 1988 Presidential contender, is looking into Mr. Spadea's case and trying to find out whether the State Department knew that the guns were destined for the rebels, not the Soviets.