The record $1.35 billion payment to depositors in two failed California savings institutions is likely to renew debate over how long the fund that insures thrifts can last without congressional action.

So far, the Federal Savings and Loan Insurance Corp. has gotten by without taxpayer money. Congress last August provided for an infusion of $10.8 billion over three years, to be raised by sale of bonds paid off by the industry. The Federal Home Loan Bank Board, the agency in charge of thrift institutions, has used $2.9 billion of that borrowing authority.The FSLIC, which guarantees deposits up to $100,000, is paying $1.14 billion to American Diversified Savings Bank and $209 million to North America Savings and Loan Association. Both are located in Costa Mesa, Calif.

The American Diversified transaction is FSLIC's largest cash payout in the agency's 54-year history, according to the top federal S&L regulator, M. Danny Wall chairman of the Federal Home Loan Bank Board.

The agency has spent more on assistance transactions, including $2 billion a month ago to help Southwest Savings Association in Dallas acquire four insolvent S&Ls, and $1.3 billion in November to bail out Vernon Savings and Loan Association, also of Dallas.

But in those cases most of the help came in the form of notes, promising payment if needed, and guarantees against certain future losses.

The two California transactions drop the insurance fund cash balance from $3.2 billion to $1.9 billion. However, another $465 million in revenue is due this month from insurance premiums paid by healthy S&Ls.

All told, including insurance premium payments by S&Ls, the fund should have about $20 billion to work with over three years and about $30 billion over 10 years.

However, the General Accounting Office, Congress' investigating arm, warns that may not be enough. About 500 of the nation's 3,120 federally insured S&Ls are considered insolvent and the GAO says it will cost $26 billion to $36 billion to clean up the mess.

Private analysts put the price tag even higher - at about $50 billion.

Problems ahead for the thrift industry include Texas, where 143 of 281 thrifts are ailing. Sunbelt Savings Association in Dallas alone recorded a $1.2 billion loss in the first quarter of this year.

In California, the rescue of the second largest S&L holding company in the nation, Financial Corp. of America in Irvine, is still pending. The Robert M. Bass Group of Fort Worth, Texas, is negotiating with the bank board over a takeover. Estimates of the cost of that bailout run into the billions.

Wall says the bank board has all it can responsibly spend through 1990. But should more money be required, there are basically three sources where Congress will look.

The first is the industry. George Gould, undersecretary of the Treasury, estimates the industry could finance something less than $15 billion. That's vigorously opposed by the S&L lobby groups.

The second is the Federal Deposit Insurance Corp., which has $18 billion to insure deposits in 13,650 commercial banks. Commercial banks and their regulators are already moving to try to head that off.

The third source would be tax funds, not an easy proposition to get by Congress in an age of budget limits.