Postal contract bargainers fighting a Thursday midnight deadline and the possibility of strikes or slowdowns, bogged down yesterday over the highly devisive issue of worker layoffs.

But federal negotiators were meeting separately with both sides, and rejected suggestions of a contract deadlock.

One of the major points at issue was a demand by the Postal Service that the three unions, representing more than 500,000 postal workers, agree to scrap or modify an existing "no-layoff" clause under which jobs can be reduced only by attraction.

Union sources said bargaining was reduced to "paper-shuffling" when Postal Service negotiators insisted on discussing the no-layoff provision before taking up other major issues.

The unions reportedly balked, and at one point Emmet Andrews, president of the 300,000-member American Postal Workers Union, prepared a statement for release to his officers saying the talks had broken off.

After federal mediators interceded, the statement was modified, although Andrews was still telling union members in a recorded telephone message late yesterday that the unions were "up against a stone wall" in the talks.

Both the Postal Service and federal mediators minimized the signifiance of the dispute, emphasizing that negotiations - apparently of an arms-length variety that is not unusual in contract bargaining - were still under way.

"There has been no breakoff. The parties are meeting separately with us at our request," said Wayne L. Horvitz, director of the Federal Mediation and Conciliation Service.

Horvitz said "a lot of progress" had been made on many issues over the previous week, but acknowledged that "there are some difficult ones still on the table." These are understood to include money and job security, the key issues in the negotiations.

A Postal Service source said: "We're still negotiating, and we have our fingers crossed."

A union source, agreeing that the talks were not broken off characterized the bargaining slowdown as a "tactical interruption" by the Postal Service to make a settlement as "tough and white-knuckled as it can be."

Negotiations between the Postal Service and the three unions - the APWU, the Letter Carriers and the Mail Handlers - are expected to go down to the wire. If an agreement is not reached by early Friday, strikes or slowdowns are possible, although they are illegal.

Federal law calls for dismissal of postal workers who strike, along with possible fines and jail sentences, but no punishment was meted out when about 200,000 postal workers struck in 1970 during a bargaining dispute.

Yesterday postal workers began receiving letters from Postmaster General William F. Bolger warning that strikers would "forfeit their right to hold their postal jobs" and lose health and life insurance coverage and other fringe benefits. The Postal Service, he said, intends to enforce the law.

Meanwhile, the Postal Service has prepared contingency plans for handling mail during a strike, including use of military troops.

The Postal Service wants to get rid of the no-layoff clause, which was the unions' price for going along with postal reorganization in 1970, in order to facilitate mechanization and reduce costs. The unions argue that the Postal Service has cut nearly 74,000 jobs through attrituion since 1971 and say their workers lack job security protections afforded other government workers. Both sides have reportedly taken rigid positions on the issue, and sources have said a strike, if it comes, is more likely over this than money.

The unions are seeking an increase of roughly 14 percent a year over two years, while the Postal Service has offered a three-year package that reportedly would cost well below the White House goal of 5.5 percent a year for all government workers, including employes of the quasi-independent Postal Service.