For lack of $30,000 for an agency caught in a budget crunch, the Defense Department has a little problem on its hands.

The department is trying to hold union representation elections for 7,000 of its employes who work in the Panama Canal Zone.

And it wants to do it before March 31, when, under the 1978 Panama Canal Treaties, Panamanian laws apply along with U.S. laws in areas of U.S. operations.

Normally, the Federal Labor Relations Authority would simply fly a team of officials down to conduct the elections.

But the FLRA's budget got chopped in last fall's continuing resolution, and agency officials don't want to spend 10 percent of their travel budget for the year on one group of elections.

More than 75 percent of the 7,000 affected workers are native Panamanians, and the Panamanian government has indicated that it wants some control over unions representing its citizens, White House and Defense Department officials said.

"There is concern that we could create the appearance of challenging the sovereignty of the government of Panama" by conducting the elections under U.S. regulations after March 31, said Thomas Garnett, deputy director for labor relations in the Defense Department's office of civilian personnel policy.

He said the government wants to avoid "any appearance" of that.

Three U.S.-based unions are competing for the right to represent civilian employes at four military installations in Panama: Army, Air Force, Navy and an Army-Air Force exchange. The unions include the American Federation of Government Employes; Local 907, a Panamanian workers' affiliate of the American Federation of State, County and Municipal Employes, and the National Maritime Union of America.

William Schrader, chief of labor and employe relations for the U.S. Army, said Defense officials "are working right now on an alternative" to conduct the elections between March 16 and March 26. In meetings with FLRA officials last week, "It became quite clear that they've been cut so badly" in the budget process that "they need some help," he said.

FLRA agents normally travel to federal employe election sites to set up polling places, monitor voting and count the ballots after the voting.

But the tiny office, with about 200 employes nationwide, had its $1 million travel budget for fiscal 1981 cut to $300,000 this year. The agency figures it would take 16 employes, at a cost of $30,000, to hold the Panama election.

FLRA general counsel H. Stephan Gordon said the FLRA could allow the Defense Department to supervise the elections with the assistance of two or three FLRA officials. But supervised elections take longer to organize than those the FLRA conducts completely, and that could push the Panama races beyond March 31, Defense officials said.

"From our viewpoint, we feel it is best to have the elections conducted by the FLRA," Garnett said.

"They have the expertise . . . . Having them do it removes the potential for problems that could come up without them."