After getting strong signs of opposition to the 50-cent-a-gallon gasoline tax increase it is considering, the Carter Administration is exploring whether a fee of $5 or so per barrel on imported crude oil might instead be used to cut gasoline consumption, officials said.

The 50-cent tax increase would require legislation, while some officials believe an import fee could be imposed without Congress becoming involved.

The tax idea has not been killed, officials said, but analysis of the proposed import fee is taking precedence at the moment.

Such a fee, which President Carter could impose, would increase the cost of foreign crude oil to American refiners. To make sure those costs would fall on gasoline and not other products, such as home heating oil, the program for equalizing crude costs to refiners -- known as the entitlement program -- would be utilized.

Getting rid of the entitlements program, however, was one idea the administration had when it ordered phased decontrol of domestic crude oil prics ending in October 1981. Adopting the import fee approach to cutting gasoline consumption would probably mean the entitlements program would have to be continued, and in a more complicated form, officials said.

A $5-per-barrel fee, if its entire impact were felt in gasoline prices, would increase prices at the pump by about 13 cents a gallon. If domestic crude oil prices were allowed to rise in line with imported oil, and that, too, were loaded on gasoline, the increase could approach 30 cents a gallon.

Carter has said he also is considering some form of rationing to reduce gasoline consumption.

Treasury Secretary G. William Miller and James McIntyre, director of the Office of Management and Budget, are said to favor the 50-cent tax proposal. Presidential aide Stuart Eizenstat reportedly opposes it on politicial and economic grounds.