Three unions, representing some 675,000 workers, went on strike against the American Telephone & Telegraph Co. at 12:01 a.m. today after failing to negotiate a three-year contract.

AT&T officials said that supervisory personnel will operate telephone switchboards and customers will experience few immediate problems. However, they said delays should be expected in getting operator assistance.

The Chesapeake & Potomac Telephone Co., which provides service in the Washington area, said it will "make every effort . . . to provide high quality service" with management and supervisory personnel.

A C&P spokesman said the company has about 32,000 union employes and about 11,000 persons in managerial and supervisory posts in Maryland, Virginia, West Virginia and the District.

Leaders of the Communications Workers of America, the International Brotherhood of Electrical Workers and the Telecommunications International Union called their members off the job after contract negotiations between the unions and the company proved unsuccessful.

CWA President Glenn E. Watts said that his union's executive committee had "voted unanimously that we should go on strike as planned....

That announcement followed the three unions' rejection earlier in the day of a revised contract package by AT&T.

Watts pulled his 525,000 members off the job under the union's "no contract, no work" tradition.

The CWA's previous three-year contract expired at midnight in each time zone.

The CWA's last nationwide strike against AT&T was in 1971.

Formal negotiations between the CWA and AT&T broke off after the union rejected the company's revised wage package yesterday morning.

Nevertheless, informal negotiations continued at Washington's Mayflower Hotel until 11 p.m., one hour before the strike deadline, when the talks again broke off.

Union spokesman Duayne Trecker said that Watts and the CWA executive board had met throughout Friday night and found the company's revised proposals "totally unacceptable."

Trecker said that the rejected wage package called for no immediate raise for the lowest pay rate to a 3.5 percent increase at the maximum pay level, and included a cost-of-living formula identical to that in the present contract.

The phone talks are the largest labor negotiation scheduled for this year. In a number of the major negotiations last year, in such industries as autos, trucking and steel, unions settled for small gains and even agreed to "give-backs."

But those were troubled industries, and the CWA says that the phone company is different because its profits have been healthy.

The bargaining has been made more complex by the court-ordered divestiture by AT&T of its 22 operating companies by the end of this year.

Watts had said Friday that AT&T would have to more than double its last wage offer to avert a walkout.

AT&T spokesman Charles Dynes had voiced confidence early Saturday that an agreement would be reached before the strike deadline, but said that a strike would not have a major effect immediately on service to the system's 150 million telephones.

"Most people dial their own calls. And I don't think they'd see any effect," Dynes said.

"If there were a strike . . . an awful lot of people who otherwise would have a free weekend would go to work . . . behind switchboard consoles, working on dial equipment and other things," he said.