Chrysler Financial Corp., the credit arm of the financially troubled Chrysler Corp., is attempting to qualify as a special government-approved lender so that it can provide federally guaranteed loans to its dealers. If approved, the move could ultimately make available $550 million for consumers to buy Chrysler products during the current period of tight credit.

Edwin O. Grote, executive vice president of operations for Chyrsler Financial, said his firm was working with the Small Business Adminstration to qualify as an SBA lender. It would then be able to offer wholesale inventory financing to its economically strapped dealers, and then sell those loans in the secondary market used for SBA-guaranteed interest certificates. Funds would then be available for Chrysler customers whose inability to obtain credit has aggravated Chrysler's problems, Grote said.

Grote said two other finance companies have previously participated in SBA's lending programs, and Congress would not have to appropriate any more money for the agency. The company is preparing its application now, Grote said.

Grote was among several U.S. auto dealers and bankers who testified yesterday before the Senate Select Committee on Small Business on problems plaguing the nation's auto industry and Chrysler in particular.

The representatives drew a dreary portrait of that industry -- faced with continued low sales, increased penetration by gas- efficient imports, less credit for dealers and consumers, more car repossessions, dealer bankruptcies and the reality that probably little can be done to help them.

The auto dealers, from North Carolina to Maine, asked Congress for temporary federal aid to relieve their plight until they can get rid of their larger and larger inventories of unsold cars.

The dealers said that high interest rates have made credit unavailable for potential customers. Low car sales have forced the dealers to finance, also at high interest rates, growing numbers of unsold cars.

Sen. Robert B. Morgan (D-N.C.) said there is probably nothing Congress can do to help the dealers. Sen. Dale Bumpers (D-Ark.) blasted the automakers for not being farsighted enough to start producing gas-efficient cars before imports began capturing the U.S. market.

"The automakers are forcing the dealers into bankruptcy by forcing them to take (large gas-guzzling cars) they can't sell," Bumpers said. "There's nothing this committee can do for you.

"If I were an American auto dealer . . .I'd certainly try to hustle me an import franchise," Bumpers continued. "I think it's a tragedy of mammoth proportions and you dealers are being victimized."

The SBA was charged by Congress last January to study the problems of the auto industry in general and Chrysler in particular as part of Chrysler's $3.5 billion federal aid program.

Larry Swenson, a South Dakota and Minnesota car dealer, said that in Minnesota 14 dealers have closed since January, including the third largest Dodge dealer in the nation.

Terry Massef said that of 116 Ford dealers in the Lansing, Mich. area, 45 have said they are in "immediate need of cash assistance and could go out of business in the next 90 days."

Wendell Miller, president-elect of the National Automobile Dealers Association, said that nationwide 500 of 4,800 Chrysler dealers have folded in the last nine months, compared to 400 that closed during last year. He added only two of five potential customers who would have obtained credit to buy a car last year can get credit now.

Banks are telling dealers, Miller added, "Look, we just don't care to have your business."

Despite President Carter's promises last month that car sales and small business people wouldn't be hurt by his credit-tightening program, Maine auto dealer Shep Lee said that Carter's program would "break the backs of small business before it will break the back of inflation."