If the telephone workers' strike against American Telephone & Telegraph Co. continues for more than a month, it could pose serious planning problems as the company attempts to meet the Jan. 1 deadline for its court-ordered breakup, Bell System executives, union officials and analysts said today.

In some parts of AT&T, key executives are spending time serving as phone operators, and although the company's financial, network and strategic efforts have not yet been delayed by the 10-day-old strike, a prolonged work stoppage could raise serious questions about the company's ability to meet the divestiture deadline, these observers say.

"As far as divestiture, one-one-eighty four January 1, 1984 is our target date," AT&T President William M. Ellinghaus said today. "We've made no changes in that. Our planning is not affected."

But Ellinghaus went on to say that if the strike were "prolonged" for several months, the "tight schedules" for completing complex divestiture planning assignments might be altered by the strike. "I'm sure it could happen," Ellinghaus said. "I'm sure there are some areas where we may have to move away from some planning work."

AT&T officials noted pointedly today that, although they have set Jan. 1 as the target date for divestiture--a date picked for its value as the beginning of the company's fiscal year--under the terms of the divestiture decision by U.S. District Judge Harold Greene, they actually have until late February 1984 to complete the breakup, 18 months after the entering of the court's divestiture order.

Although the company and the Communications Workers of America announced today that representatives of the two sides would hold their first formal bargaining talks Tuesday, neither side expressed hopes for an imminent settlement.

"I think it's going to be a long strike," said James Mc Cabe, an analyst with Prudential-Bache Securities Inc., a prediction other industry analysts shared yesterday. "It's difficult to negotiate job security. The company sees the opportunity to significantly reduce the labor force. They are not going to cave in."

He also noted that even delaying divestiture by several months could significantly alter the immediate competitive positions of the seven operating telephone companies AT&T will spin off under its consent decree with the Justice Department. "If they can't do what needs to be done, it would hurt because the more uncertainty, the more it would impact the stock prices," McCabe said.

Spokesmen for several local phone companies said today that their divestiture planning was continuing, particularly the complex financial restructuring the effort entails. Yet some key planners on the local level are clearly altering their duties because of the strike.

For example, Dana Campbell, chief spokesman for Southwestern Bell in St. Louis, said that when he called the divestiture network and operations planning office at his company, he could not "get anybody to answer the phone."

Campbell said that most of the members of that office are "out working the switch boards or are out on installations," but that the company had not yet fallen behind in its planning efforts. "Nobody is really worried right now, but if we go on for a few more weeks, it may cause problems," he said.

Among those potential problems is the possibility that state regulators might be called upon to reconsider pending local rate increases or figure in the impact of the strike on those proposals. At a time of dramatic change within the telephone industry, with at least $13 billion in rate hikes now before state utility regulators, there is mounting public pressure on those panels to carefully monitor those requests.

In New York, an effort already is under way to link rate cases to strike action. New York State Attorney General Robert Abrams said over the weekend that New York Telephone Co. is saving $30 million a week on labor costs and that the state's Public Service Commission ought to suspend rate tariffs and investigate the possibility of actually reducing local phone rates here.

CWA officials said the efforts like the one initiated by Abrams might take on more steam with union support, a program that CWA President Glenn Watts said "sounds logical."

Further complicating the negotiating effort is the fact that AT&T's top negotiators appear to be checking for approval from top officials of the to-be-divested regional companies, firms whose interests are rapidly parting from those of AT&T's top management.

"A lot of the regional companies are doing a lot of thinking about whether they want nationwide bargaining," said Winston E. Himsworth, a first vice president with Lehman Brothers Kuhn Loeb Inc.

Analysts also noted that the company's per share profits could be boosted by anywhere from 7 to 10 cents for each week the strike continues. The financial analysts suggested that, therefore, some of the local companies might have short-term incentives to delay negotiating because they could subsequently offer improved balance sheets to the financial community when they gain their independece at the time of divestiture.