In a move that could get it out of legal quicksand, and win the hearts of 300,000 federal commuters from Sacramento to Silver Spring, the Reagan administration is studying the possibility of shutting down Uncle Sam's pay parking lots for keeps.

Earlier this month a federal District Court judge here ruled that the Carter pay parking plan (begun in late 1979) was illegal because Congress was not consulted. The program required several hundred thousand U.S. civilian workers -- including 75,000 here -- to pay for spaces they once got free. Under the plan employes were to pay one-half the commercial equivalent parking fee for the first two years of the program, and then go to full fees this fall. Locally those fees ranged from $12 to $40 per month.

The American Federation of Government Employees, later joined by the National Treasury Employees Union, argued that employes should be reimbursed about $25 million -- about $340 per person -- for fees paid between the fall of 1979 and this month. Later this week Judge Harold H. Greene will hear arguments from the government and the unions on the payback.

Washington area legislators -- Virginia Republican Reps. Stan Parris and Frank R. Wolf, and Maryland Democratic Congressman Mike Barnes -- want the pay parking program killed for good. The day after the Inauguration, Wolf contacted top Reagan aides and pointed out that some Army privates who live off post now have to pay $12.50 a month to park.

Wolf and Parris said that administering the pay parking program in some agencies -- including personnel to allot stickers, printing of signs, records collection and the like --costs more than it makes.Nearly everyone agrees that the pay parking makes federal workers angry, and works a hardship on low-paid workers who must commute long distances and pay, even for running large car pools.

As reported here March 11, the administration already has ordered federal agencies to turn on hot water taps that had been shut off locally by the General Services Administration in June 1980.

With that example in mind, Parris believes there is a good chance the White House will order government attorneys to withdraw their appeal of the Greene decision covering pay parking.

A congressional source who asked not to be identified said that the three congressmen -- whose districts are swarming with federal and military voters -- have been steadily urging White House aides to turn the hot water back on (that is happening now) and stop the pay parking program. "They have told White House congressional liaison people and Reagan aides to ease up on federal workers, particulary since they are going to be hit hard by job cutbacks, pay raise cutbacks and other budget items," he said.

Union officials contacted yesterday say they have no information on the White House intentions. And they say no deals have been sought. But they would welcome the action -- the unions think they can win the appeal anyhow and kill pay parking permanently -- and they will continue to seek restitution for fees already paid.

With the major government changes Reagan is seeking, he can use all the inside help he can get from the bureaucracy. Dropping the pay parking plan -- something he inherited from the Carter administration -- wouldn't hurt his stock in government. And it might actually save Uncle Sam some time and money.

Some of the programs agencies have set up to police the pay parking program border on the ridiculous. Special police have been assigned to give out tickets to violators, and new offfices -- some staffed with temporary workers -- have been set up to process passes, collect money and do the increased bookkeeping and paperwork that the program has created.