New labor problems threaten to shut down The New York Times and The New York Daily News this week.

The photoengravers union has set a midnight Monday strike deadline in its talks with the two papers, which are bargaining jointly as members of the Publishers Association.

Warren Bush, financial secretary of the photoengraver's local, said the publishers are refusing to give photoengravers the same job security that has been extended to other craft workers, most recently to the pressmen at the end of their 88-day strike last year.

Spokesmen for The Times and Daily News argue that the photoengravers have been offered as much as other craft unions have received and are demanding more. All New York craft union contracts have "me too" clauses, which guarantee that they will get any benefits won by any other union. Therefore, if the tiny photoengravers union won special provisions these would have to be granted to thousands of other workers.

There are 160 photoengravers at the Daily News and 31 at The New York Times. The New York Post, the city's third paper, has no unit of the photoengravers union.

The main problem in negotiations has been the Daily News' color printing plant at Newspoint in Queens. The plant has lost money since it opened, according to a News spokesman, and now seeks to do commercial printing jobs in addition to producing the comics and Sunday magazine for the News. The spokesman said the company is asking photoengravers for concessions that would enable the Newspoint plant to be competitive with other commercial printing plants.