The Reagan administration and federal employe unions failed to reach a compromise yesterday on flexitime legislation, virtually assuring that the government's experiment with four-day work weeks will be shut down by March 29, according to union spokesmen and several congressional sources.

A Senate bill that would have authorized continuation of alternative work scheduling programs for more than 325,000 U.S. employes, including about 175,000 workers who are on a four-day work week, was sent to committee rather than voted on after union representatives and administration officials disagreed over the terms under which flexitime programs would be started or stopped.

"It's flexitime pretty dead," said an aide to Sen. Ted Stevens (R-Alaska), sponsor of the attempted compromise measure.

The compressed work week and other programs that deviate from the traditional eight-hour day, 40-hour week are set to expire March 29 unless Congress extends or makes permanent its three-year experiment with flexitime. Employes who stagger the starting and stopping times of their eight-hour days or employes whose flexitime programs were negotiated as a part of their union contracts will not be affected by the deadline.

The Stevens aide said the administration wanted to have more control over starting and stopping the programs, while the American Federation of Government Employees said the programs should be allowed as long as they did not reduce productivity, hinder public service or increase agency costs.

The entire issue had been bogged down for weeks over similar disagreements about management control versus employe rights in negotiating such working arrangements.

Gary DiNunno, an AFGE spokesman, said the union objected to the Stevens bill because it would have invalidated already negotiated flexitime agreements. "We'd rather see the whole thing go under than have our contracts thrown out," he said.

Pat Korten, spokesman for Office of Personnel Management director Donald J. Devine, blamed union "intransigence" for the collapse of a flexitime compromise. He said OPM wanted to continue alternative work schedules but "could not allow a situation where the automatic presumption was against management."

AFGE plans to push for passage of another, "more acceptable" flexitime bill sponsored by Rep. Geraldine Ferraro (D-N.Y.) But her legislation has been stalled in the House, and flexitime supporters said yesterday it is doubtful any measure can get through Congress prior to the March 29 expiration date.