A 13,000-member Teamsters Union local has begun a determined and well-financed effort to organize maintenance and service workers at a Northern Virginia hospital.

If the drive at Alexandria Hospital is successful, the union says it will launch organizing campaigns among workers at other hospitals in the District, Maryland, and Virginia.

The Teamsters' efforts at the non-profit Alexandria Hospital are bitterly opposed by hospital officials, who contend the union would drive up patient costs there. The campaign is being watched closely by rival labor unions and other hospital administrators, anxious to see if the militant union can win its first victory in the area among health-care workers.

"Alexandria is simply a stepping-stone for us," said Ben Hylton, secretary-treasurer of Teamster Local No. 246, yesterday. The local has committed $12,000 to its effort to win the support of 500 workers at Alexandria Hospital in an Oct. 19 election.

Officials of the 414-bed facility on Seminary Road are adament in their opposition to the Teamsters. "We are opposed to the Teamsters coming in here," said spokesman Dave Norcross yesterday. "The cost of patient care will increase, and we are greatly concerned that the quality of patient care will go down."

But Hylton argues that the Alexandria workers "have been ripe for organizing since July."

That's when the hospital fired 30 longtime employes in what Norcross said was an "economy move" designed to offset an anticipated $4 million deficit. The hospital has suffered a "troubling" decline in patients in recent years, he said.

This year 14,500 patients will spend at least one night there, a 5 percent decrease from the previous year, and the number of emergency room patients will drop 10 percent, Norcross said.

Officials attribute part of the decline to the 1977 opening of Mount Vernon Hospital, in Northern Fairfax County, near the Alexandria border.

Norcross said the hospital is countering the Teamsters campaign by arguing that the union would form "an unneeded layer" between the workers and the hospital administration.

"We tell them (the employes) that it is not in the best interest of the hospital or the community to have unions in here," Norcross said.

A 1975 attempt by the Communications Workers of America to organize Alexandria Hospital employes failed, but Teamsters represented police in several Northern Virginia localities before a state court barred collective bargaining by Virginia municipalities.

The American Federation of State County and Municipal Employes represents about 5,000 hospital workers in the service and paraprofessional fields at hospitals in the District of Columbia and Maryland according to union spokesman Mike Dowling. Other unions representing area hospital employes include the District of Columbia Nurses Association and the National Union of Hospital and Health Care Employes, District 1199.