More than 120 pieces of legislation pending in the U.S. Congress have a single aim in mind -- to stimulate deposits in the savings and loan institutions that make mortgage loans for prospective homebuyers.

Members of Congress appear to have recognized that something must be done rapidly to help solve the problems of the nation's hard-pressed thrift institutions, since only the president's economic recovery program has generated a greater number of pieces of proposed legislation.

Among them, for example, is a bill introduced in the House by Rep. Bill Archer (R-Texas) that attempts to help mortgage lending institutions and also reduce the cost of mortgage money to homebuyers by as much as 3 or 4 percentage points. Similar legislation has been introduced in the Senate By Sen. Lloyd Bentsen (D-Texas).

In addition to being saddled with more than $80 billion worth of mortgages yielding less than 8 percent, the savings and loans also are continuing to lose large blocks of higher-cost certificate money to money market mutual funds paying higher rates.

Rollin Barnard, president of the U.S. League of Savings Institutions, recently told the house Ways and Means Committee that a new tax-exempt "investment certificate" is needed to attract lower-cost funds that would be pegged below Treasury securities. In turn, lower mortgage rates would result because of the lesser cost of getting funds.

Herman Smith, president of the National Association of Home Builders, applauded the "investment certificate" approach in his testimony, adding that "what is good for the thrifts is good for housing and good for the country."

Smith also told the House Budget Committee that the "missing ingredient" in the administration's tax plan is a pattern of tax incentives that would create a new savings ethic among Americans. In general, Smith urged legislation that would give tax-free treatment to all savings used directly for residential mortgages.

Although this could result in a substantial loss of revenue for the Treasury, some observers believe the loss might be less than the amount some other branch of the government might have to spend to either bail out or support ailing thrift institutions that have been losing money, customers and prestige.

The NAHB's Smith and others also contend that the tax-free savings plan would stimulate construction of an additional 600,000 housing units annually, thus creating 860,000 man-years of employment and $8 billion in federal tax revenue. It's a matter of putting people back to work and having them pay taxes rather than being on the unemployment benefit rolls, Smith testified.

Housing starts, which for nearly 18 months have been depresed except for brief spurts, fell to an annual rate of 1.2 million units in February. Fewer than 1.3 million dwellings were started last year.

Housing industry sources predict no increase in new construction this year due to the high cost of construction loans, which are usually 2 points above the prime rate. Additionally, both new and existing house sales are inhibited by the high level of both FHA-VA (14 percent) mortgages and conventional (14 1/2 to 15 1/2 percent) loans for home purchasers.

Sales of new houses are reported to be 17 percent below those of 1980, and resales also are substantially below the peak level of 1979. Nonetheless, the real estate information arm of the business publishing firm of McGraw-Hill has predicted that 3.2 million existing single-family homes will be resold this year, an increase of 11 percent over the depressed 1980 level. McGraw-Hill also declared that latent consumer demand and lower interest rates would improve residential sales in the last three quarters of 1981.

In the Washington area, P. Wesley Foster Jr., president of Long & Foster with 36 branch residential brokerage offices, reported that the areas of Washington in which average prices were highest last year were McLean ($153,386), Potomac ($149,290), Uptown/NW D.C. ($128,436), Great Falls ($116,321) and Vienna ($109,379).

The Long & Foster statistics showed lowest average prices -- ranging from $52,246 to $68,640 -- in Fredericksburg, Va., and in Frederick, Andrews, Waldorf and College Park, Md.