Congress gave a frosty reception yesterday to another of President Carter's key budget-balancing proposals -- his plan to require withholding of taxes from interest and dividends on savings and corporate securities.

At a hearing of the House Ways and Means Committee, liberals and conservatives took turns lambasting the plan, charging it would burden business unduly and discourage needed savings and investment.

After only a handful of panel members supported the measure, Rep. Bill Frenzel (R-Minn.) told administration witnesses: "If you can sell this sow's purse to the commitee, I'm going to give you the Harry Houdini award."

Immediately after the administration presented its case, the committee was bombarded with testimony from more than a dozen banking industry and stockholders' groups also opposing the withholding measure.

The rebuff marked the second time one of the president's major revenue-raising measures faced serious opposition in Congress. Last week, Ways and Means Committee members indicated they may try to roll back Carter's new oil-import fee.

If the lawmakers reject both proposals, it would add $13.7 billion to the federal budget deficit for fiscal 1981 and dampen prospects for balancing the budget with a surplus large enough to allow a tax cut.

Carter proposed both the import fee and the tax-withholding measure as part of the budget-balancing plan in his March 14 anti-inflation package.

The tax-withholding plan was endorsed by White House-congressional negotiators, but although Ways and Means Committee members supported Carter's move to balance the budget for fiscal 1981, they have opposed the oil-import fee for raising gasoline prices and have criticized the tax-withholding plan as a tax hike.

Treasury Secretary G. William Miller argued that the plan to withhold taxes wouldn't amount to an actual tax increase for savers and investors, but only would step up collection of taxes there persons already owe.

The Treasury estimated yesterday that investors failed to report some $16 billion in interest and dividend income in 1976 -- either inadvertently or on purpose to evade taxes -- a rate of noncompliance 300 times that for wage income.

Miller told the Ways and Means panel that to crack down on abuses in this area without requiring tax with holding would take "millions of telephone calls, letters and visits" and would "inevitably be regarded as harassment."

However, committee members asserted that the withholding plan would put a burden on banks and businesses and would cut into investment. Rep. Thomas Downey (D-N.), a liberal, said Carter was proposing the move at the wrong time.

Opposition from industry trade groups also was vigorous. C.C. Hope Jr., president of the American Bankers Assn, charged the plan would "deter savings, impose new cost burdens and . . . cannot be made to apply fairly" to all savers.

And Richard S. Lawton, vice president of the National Savings and Loan League, branded the plan an "ill-conceived . . . gimmick." Lawton contended the noncompliance problem involved only "a small number" of savers.

The only major support for the tax-withholding plan came from the AFL-CIO, which wants the proposal enacted to ward off still-sharper cuts in domestic spending, and from the Ralph Nader-affiliated Tax Reform Research Group.

Hope's opposition was a turnabout for the American Bankers Assn president. The Atlanta banker had called reporters March 15 to announce that his group would endorse the tax-withholding plan.

The outlook for the oil-import fee also is uncertain. Carter told a group of lawmakers on Saturday he would veto any measure designed to repeal the new levy, but it is unclear whether the two houses would override him.

The proposal for tax withholding would require finanical institutions and corporations to take out 15 percent of all taxable interest and dividends paid to individuals, including that on Treasury bills, coupon bonds and government agency issues.

Miller estimated yesterday that enactment of the new plan would increase Treasury revenues by $3.4 billion in fiscal 1981, $2.2 billion in fiscal 1982 and $2.5 billion in fiscal 1983, mostly by cracking down on noncompliers.