The National Savings and Loan League yesterday urged Congress to approve a program that would provide an estimated $15.5 billion in short-term financial assistance to the troubled S&L industry.

The league, which is the trade association for most of the nation's larger S&Ls, developed the program at its annual governmental affairs conference that ended here yesterday.

The league renewed its call for passage of pending legislation to restructure the savings industry, but said that legislation would help the industry in the long run, and direct financial assistance is needed sooner.

The main element of the capital assistance program for troubled associations is a plan for the federal government to warehouse low-yielding mortgages until interest rates decline.

As outlined by the league, a federal agency, such as the Federal Savings and Loan Insurance Corp., would issue debentures to S&Ls in exchange for their low-yielding mortgages. The debentures, on which S&Ls would receive interest, would bear a variable interest rate tied to the 30-month Treasury bill rate.

S&Ls would exchange the debentures at maturity in three to five years for their low-yielding mortgages.

League officials estimate the cost of the warehousing program at $8 billion over a three- to five-year period, assuming that interest rates fall.

The second part of the league's program calls for capital assistance designed to increase mortgage lending and boost the housing industry. The league endorsed in principle a bill introduced yesterday by Rep. Fernand J. St Germain (D-R.I.), chairman of the House Banking Committee, that would appropriate $7.5 billion over three years for cash infusions to home mortgage lenders whose net worth falls below 2 percent of assets. The bill would require institutions that receive the assistance to earmark no less than 50 percent of their new deposits in residential property.

Although St Germain outlined his proposal at the conference this week, league officials decided to endorse it only in principle until they have had a chance to study the bill.

The third part of the league's program calls for broadening tax incentives for savers, including an extension of the All Savers certificate beyond Dec. 31.

League officials appeared confident of sufficient support in Congress for the ambitious program, despite concern on Capitol Hill about the size of the projected budget deficit for the next fiscal year.

The bill to restructure savings institutions, which the league said would provide long-term help, incorporates proposals by the Federal Home Loan Bank Board and was introduced by Senate Banking Committee Chairman Jake Garn (R-Utah). But it has been stalled in committee since late last year.