The House failed yesterday to extend legislation (expiring March 29) that allows 175,000 federal workers to waive overtime and put in longer days so they can work four-day weeks. Although the vote was 255 to 142 in favor of keeping the flexible work hours program, it fell short of the two-thirds majority required when legislation is taken up under a suspension of House rules.

Backers of the flexible-work-hours program wanted the vote taken under a rules suspension to prevent the Reagan administration from offering "crippling" amendments.

The administration says it favors the four-day week and other flexitime programs. But it wants tighter management controls so that the Office of Personnel Management decides who is covered. Currently many flexitime and four-day week plans are determined by contract, based on union and management negotiations.

An administration-backed bill giving OPM control of the program may be introduced today in the Senate.

Meanwhile, backers of the bill rebuffed yesterday in the House may try again to incorporate the about-to-expire experiment into law. They could put the bill, sponsored by Rep. Geraldine Ferraro (D-N.Y.), before the House under regular rules. This would allow it to be passed by simple majority vote, but also subject it to amendment by opponents. The program isn't dead yet, but it may be on the legislative critical list.