The Fairfax County Water Authority, whose 616,000 customers are under emergency restrictions, wouldn't be able to get a permit to tap the Potomac River until next summer under a timetable drawn up yesterday by Secretary of the Army Clifford L. Aledander Jr. and Rep. Herbert E. Harris II (D-Va.).

The timetable drew an outcry from Fairfax County Board Chairman John F. Herrity, who declared, "there's no way we could wait that ling for a permit . . . Something else has got to be worked out."

On Sept. 30 Harris, after a meeting with an official of the Army Corps of Engineers, which must decide on the water authority's application, said he saw no reason why a conditional permit couldn't be granted in 45 days.

After meeting yesterday with Alexander on Capitol Hill, Harris said, "We have worked out a schedule that we think can mean an early solution."

Under the schedule, the Corps of Engineers would complete work on its environmental impact statement on the Potomac project by Dec. 15. Public hearings would be held in January or February.

Then, "by early next summer, certainly no later than July," according to Harris, the corps would be able to grant the water authority a permit.

If the authority has to wait until next summer for a permit, its Potomac intake and treatment facility - planned as a supplement to the already over taxed Occoquan Reservoir - wouldn't be completed and operating until early 1981. The authority has said that without the Potomac supply, it might not be able to meet projected demands as early as the summer of 1980.

Informed of the timeable drawn up by Harris and Alexander, Fairfax Board Chairman Herrity said: "That's a big ripoff. They've got to be kidding. There's no way we could wait that long for a permit . . . Something else has got to be worked out."

Herrity, after a meeting yesterday with virginia Gov. Mills E. Godwin, said the governor had agreed to try to meet with acting Maryland Gov. Blair Lee III and Secretary Alexander withing two weeks on the water authority's problems getting a permit.

Alexander said he would ask Godwin, Lee and D.C. Mayor Walter E. Washington to meet at his office on the main issue holding up a permit - a regional agreement dividing up Potomac water for the rare times when the river's flow cannot meet demand.

Alexander said yesterday that "the first step is for the jurisdictions to sit down and discuss what is in equitable agreement."

Virginia and Maryland have already signed an agreement that would give the Fairfax Water Authority and the Washington Suburban Sanitary Commission (which supplies the Maryland suburbs) an increasin share of low-flow water and, consequently, less to the District.

The Corps of Engineers - which is in charge of the District's water supply - has refused to sign such an agreement, saying that any low-flow allocation must protect the District's needs. The corpos has pointed out that Northern Virginia and the Maryland suburbs, unlike the District, have ptential supply sources other than the Potomac.

Apparently scrapped as a result of the Alexander-Harris meeting yesterdy was the congressman's original plan calling for a conditional permit for the authority, with the low-flow dispute being worked out later. Alexander wants a low-flow agreement tied to the permit.