The White House yesterday gave 150 mayors and county executives a sympathetic hearing but no promise of support as they lobbied for legislation to halt the impact of a Supreme Court decision that officials say will cost state and local governments $2.5 billion a year.

Memphis Mayor Richard C. Hackett said the Feb. 19 ruling on federal wage requirements involving the San Antonio Metropolitan Transit Authority would cost his city $500,000 to $1 million annually in additional expenses, much of it to pay overtime to firefighters.

"I could not be happier with the response we received at the White House," Hackett said of the three-hour meeting involving representatives from the National League of Cities and the National Association of Counties. White House officials agreed to make a decision on the administration's position next month.

The groups got "a very encouraging reception," Alan Beals, executive director of the League of Cities, told a news conference after the meeting. Beals described White House sentiment as "sympathetic."

President Reagan and top aides are on the West Coast. Representing the White House at the meeting was Mitchell E. Daniels Jr., deputy assistant to the president and director of the office of intergovernmental affairs.

"There was no immediate indication" at the meeting of "what the administration would do," said Leigh Wilson, executive director of the North Carolina league of municipalities. A meeting of key Cabinet officers must take place first, and White House representatives indicated they probably would make a decision by Sept. 10, said Wilson.

The court ruling means that many municipalities that used to give compensatory time off to their police officers and firefighters instead of paying overtime no longer may do so.

It also means that volunteer fire departments that pay firefighters a few dollars a call may wind up having to treat them like regular employes, a burden that some local officials said would put an end to many of those operations.

Beals estimated the cost of the ruling at $1.75 billion a year to cities, $500 million to counties and up to$300 million for state governments.

After the court's ruling, local governments unsuccessfully urged the Labor Department, which enforces the law, to review existing regulations before applying them to municipalities.

But the department announced June 14 that on Oct. 15 it would begin investigations for violations that allegedly have occurred since April 15. Beals quoted Labor Department officials at yesterday's meeting as saying that they felt compelled by the law's restrictions to begin enforcing the regulations.

Congressional committees are expected to hold hearings next month on the bills, which are opposed by the largest public employes' union, the American Federation of State, County and Municipal Employees.