The auto industry said yesterday the proposed tax on big "gas guzzlers" would cause unemployment and could signal the end of the five or six-passenger family car.

But Senate Finance Committee chairman Russell B. Long (D-La.) made it clear to spokesman for the tee will follow the lead of the House Big Three - General Motors, Ford and Chyrsler - that he expects the committee will follow the lead of the House and vote some tax on purchase of big cars as part of President Carter's energy conservation program.

"We ought to put a tax on big cars so consumers won't demand them so much," said Long. "I don't know how we can lessen consumer demand except by a tax. People would expect to pay a premium for a Cadillac or Lincoln. They should have the privilege of buying a big car but should pay the tax."

S. L. Terry, vice president of Chrysler Corp., said the tax "would make it almost impossible to keep the family size car on the market. That is the heart of the market, but the tax would keep us from planning such a car by 1985."

Fred G. Secrest, executive vice president of the Ford Motor Co., said the proposed tax may force the industry "go to one line of cars" - just stop making big cars that might be subject to tax.

Spokesman for all three companies repeated that a tax on big cars would force plants to close and cause unemployment.

The administration asked for a tax on 1978 models that get less than 18 miles per gallon. The House delayed the tax until next year and would tax in the first year only cars getting less than 16 mpg. But the tax would go up steeply to a maximum of $3856 on cars getting less than 12.5 mpg.

Terry called the proposed tax a "punitive tax on family cars." The House bill would impose a tax of more than $500 by 1985 on a six-passenger car averaging 22 mpg, he said. Nearly 22 million households consist of five or six persons who need a large car, he said.

Roger B. Smith, executive vice president of General Motors Corp., said the impact of the tax would be greatest on middle and low-income families that rely on one large car.

The tax would be unfair to a family with one large car that uses less gasoline than two untaxed small cars, said Secrest.

All three urged Congress to reject the guzzler tax see if the industry can't convert sufficiently to smaller cars under the pressure of a 1975 law that takes effect this fall with 1978 model cars. That requires an auto manufacturer's entire fleet to average at least 18 mpg on 1978 cars and reach 27.5 mpg by 1985, or face heavy fines. The "wisdom" of that law, said Terry, is use of the fleet average which will permit auto companies to continue building some large cars while their smaller cars permit them to meet the standards.