The Teamsters Union suffered a surprising setback yesterday in its campaign to organize hospital workers in the Washington area.

Employes at Alexandria Hospital, who three months ago voted to join the union by a wide margin, rejected its efforts yesterday in a second election ordered by the National Labor Relations Board. The agency had voided the first election, ruling that the union had violated a regulation prohibiting last-minute electioneering.

The vote yesterday went against the union 237 to 171, a sharp reversal from the 210-to-149 margin it had secured Oct. 19 in the first election at the hospital. Union officials then said the victory at the 414-bed facility was the first in their effort to organize health care workers throughout the metropolitan area.

"Time is always on the side of the employer," said Ben Hylton, secretary-treasurer of Teamsters Local 246-"They (hospital management) convinced people they were better off without us," Hylton said the union would decide within five days whether to challenge the election.

Hospital administrator J. Edward Sweet, Jr. called the result "a vote of confidence" from the hospital's service and maintenace workers.

Hylton said yesterday he has "no plans" to try again to organize other workers at Alexander Hospital, or to reopen an unsuccessful organizing effort at Arlington Hospital. The union's only success in the metropolitan Washington area came Nov.1 when it won the right to represent 70 employes at the Masonic and Eastern Star Nursing Home in the District. That election is also being challenged.

Key issues in yesterday's elections were job security and hospital contributions to employe health plans. Last January the hospital fired 30 employes in an economy move.

Hospital attorney Tom Coleman said yesterday "we convinced the employes we felt as bad about that as they did. The union wouldn't have made any difference" in saving jobs, he said.

Coleman said the hospital management would attempt to work out satisfactory health care contributions with employes.