More than 70 members of Congress in a letter to the White House yesterday urged President Reagan to keep the federal government operating even if he vetoes the stopgap funding measure required to prevent a shutdown.

As Congress plodded toward passage of the stopgap measure and the president threatened to veto its final product, the congressmen called on Reagan to avert a shutdown like the one 13 months ago that, according to some congressional estimates, wasted as much as $80 million worth of government time.

Meanwhile, employes at all government departments were ordered to come to work Monday, although more than 500,000 could be furloughed by midday if there is no "reasonable certainty" that the funding measure will be signed by the president that day, according to the Office of Management and Budget.

This is the third time in 13 months that Washington's huge bureaucracy has teetered on the brink of a shutdown as the president and Congress could not agree on issues contained in the stopgap funding measure. Funding for the government ran out at midnight Friday, leaving most federal departments waiting for funds under umbrella legislation that has come to be known as the continuing resolution.

Those agencies and departments whose regular funding bills have been signed into law are not part of the continuing resolution and would not be affected by a shutdown. They include the Department of Housing and Urban Development, the Veterans Administration, the Environmental Protection Agency and the National Aeronautics and Space Administration.

The departments of Agriculture and Transportation were left in a sort of limbo. Their bills have been passed by Congress and are awaiting the president's signature.

The following departments and agencies, however, are part of the continuing resolution that is in dispute: Commerce, Defense, Education, Energy, Health and Human Services, Interior, Justice, Labor, State, Treasury, the General Services Administration, the Small Business Administration, the Office of Personnel Management and the Office of Management and Budget.

Rep. Steny Hoyer (D-Md.), who with Rep. Frank Wolf (R-Va.) mounted the Capitol Hill campaign to influence Reagan, said yesterday "it is a disgrace" that the failure of Congress and the president to agree causes government shutdowns.

The bulk of the shutdown cost comes from regular salaries paid to employes who are clearing desks, locking away papers and securing offices, rather than attending to their regular duties. A House Post Office and Civil Service subcommittee, which issued the report citing the $80 million shutdown cost in 1981, estimated that administrative costs alone were more than $5.9 million. Much of this cost is incurred in preparation even before a shutdown begins, according to Congressional aides.

Hoyer and the other 72 signers of the letter to Reagan called on the president to employ a transfer-of-funds technique he used last September when another lapse in funding threatened the paychecks of military personnel.

A White House spokesman had no comment on the letter. But OMB general counsel Michael Horowitz said that what the congressmen are suggesting "is impossible for the president" under law.

Horowitz said there is a "critical difference" between finding funds to pay military personnel, who must go on working whether the Department of Defense is funded or not, and finding money to keep the entire government operating. Under law, when funding runs out, the government must shut down all functions except certain essential ones, including military, medical care, law enforcement and air traffic control.

But even if the shutdown never materializes, the federal government will have spent time and money on the now-familiar process of preparing for one.

In the past two days, printers and duplicating machines in offices around Washington have spewed out the hundreds and thousands of furlough letters that will be needed in case there is a shutdown Monday afternoon.

At OMB, staffers worked up the three-page, single-space directive that went out yesterday across the federal bureaucracy, and they spent hours on the phone with top department officials.

At one huge department, the drill began Thursday, with a nationwide conference call to inform all the regional offices what to expect.

In other departments, the employe packets that include a 30-page pamphlet telling workers how to appeal their furloughs, were prepared. Although the furloughs may last only a few hours, under government regulations, all federal employes must receive these pamphlets on the complex appeals process.