The White House changed its tune ever so slightly again yesterday on the question of gasoline supplies, warning that while the West Coast shortage is expected to ease, overall gasoline supplies will still fall short of expected demand during the summer.

"The president doesn't want the American people to breathe some huge sigh of relief," presiential press secretary Jody Powell said of the relatively optimistic statements that emanated from the White House after the meeting Wednesday between President Carter and California Gov. Edmund G. (Jerry) Brown Jr.

Saying that he wanted to inject "a note of caution" into the national debate on gasoline supplies, Powell said that even with the improvements forecast by Carter and Energy Secretary James R. Schlesinger Jr., gasoline supplies will fall with about 5 percent short of demand over the summer.

"What's important is that we all understand that although the supply and demand figures are going to improve, we will still have that shortfall," he said.

The White House warning came as a group of House Democrats began drafting as new standby gasoline rationing plan that would limit gasoline purchases and require motorists to leave their cars at home one day a week.

Powell's comments, which he volunteered to reporters, were the latest example in the White House's often strained attempt to portray the seriousness of the nation's energy shortage.

For the last several weeks, for example, the president has offered gloomy predictions that gasoline shortages were likely to grow worse this summer and could become severe next summer.

But on Wednesday, after the meeting with his Democratic Party rival Brown, Carter sounded more optimistic. He announced a series of steps he said should alleviate the problem in California, and predicted that after gasoline supplies on the West Coast hit a low point this month they should begin to increase in June.

Schlesinger provided an equally optimistic forecast. He said oil imports are expected to increase over the summer, and that U.S. refiners will have more leeway to draw down existing crude oil stocks, allowing them to produce more gasoline.

Because of these factors, Schlesinger said, it may be possible to increase national gasoline deliveries from their current level of about 93 percent of 1978 supplies to 100 percent of 1978 supplies over the next several months.

What the energy secretary did not say-and what Powell chose to emphasize yesterday-was that because of a growth in demand, an increase in gasoline supplies to last year's levels would still leave the country about 5 percent short.

Moreover, some administration policies may work to dilute Schlesinger's forecast. While imports increase and refineries are able to use more of their existing crude oil stocks, the president has called for a substantial increase in the production of home heating fuels for next winter, leaving less crude oil available to be turned into gasoline.

The White House seems caught between competing objectives in its portrayals of the shortage. On the one hand, Carter has issued his dire predictions of worsening shortages while attempting to prod Congress into enacting his "windfall profits" tax on the oil industry and as part of his unsuccessful attempt to win congressional approval of his tandby gasoline rationing plan.

But when confronted with signs of anger and panic among motorists in parts of the country-and as part of the political byplay involved in the Brown visit to the White House-the official predictions, while stressing that the nation's "fundamental" energy problems remain unchanged, turned more optimistic on the question of short-run gasoline supplies.

On Capitol Hill yesterday, Rep. John D. Dingell (D-Mich.), chairman of a House Energy subcommittee, threw his support behind the effort of Rep. Toby Mffett (D-Conn.) to draft a rationing plan. Carter, angry at the rejection of his plan, has challenged Congress to produce its own rationing scheme within 90 days.

Among its provisions, Moffett's proposal would require motorists to leave their cars at home one day a week. Dingell said the proposal shows some promise of easing lines at service stations, adding that any measure that would distribute gasoline supplies more evenly would be welcome.

"The disaster we have upon us is real, serious and of lengthy duration,c Dingell said.

Yesterday, Dingell instructed his subcommittee staff to work with Moffett and other Democrats who are trying to draft a substitute for the rejected administration rationing plan.

Moffett has said his plan probably would set a nationwide $5 minimum for gasoline purchases to discourage motorists from "topping off" gas tanks, and would call for a state-administratered sticker system to keep each automobile off the road one day a week. CAPTION: Picture, With no gasoline to sell, these attendants are idle at a car wash-service station in Santa Monica, Calif. AP