Both houses of Congress yesterday defeated Republican proposals for a tax cut of $30 billion or more next year as they moved jointly toward approval of a balanced-budget spending target for 1981.

In both cases, the Republicans would have maintained or expanded proposed outlays for defense while slashing domestic programs to provide money for the tax cut.

By a vote of 35 to 59, with many Republicans joining most Democrats in a display of bipartisan support for their Budget Committee, the Senate rejected a proposal from Sens. William L. Armstrong (R-Colo.) and William V. Roth Jr. (R-Del.) to cut taxes by $30 billion.

Only minutes earlier, the House, voting 175 to 242 along sharply partisan lines, turned down an official Republican Party proposal offered by Rep. Delbert L. Latta (R-Ohio) to sanction a tax cut of $32 billion.

Then, the House, on a much closer vote of 191 to 218, rejected another $30-billion range tax cut proposal by Rep. John H. Rousselot (R-Calif.), which also assumed repeal of President Carter's controverisal oil import fee that will raise the pump price of gasoline by 10 cents a gallon.

The Armstrong-Roth proposal would have cut heavily into existing food stamp and job programs, along with trimming other domestic outlays, in exchange for lower taxes on savings and investments, tax adjustments to protect individuals from the "inflation creep" in tax rates and tax incentives for business and expansion.

The Republican proposal in the House was similar, although less specific. It would also have increased proposed defense spending to bring the House figure more in line with the big military spending increase that the Senate is expected to approve.

As it worked into the night, the Senate also rejected amendments to provide money the administration doesn't want for the strategic petroleum reserve and to add funds for veterans' benefits at the expense of some funds for job programs.

The budget resolutions are the first step in Congress' six-year-old spending discipline procedure, but this year stiff enforcement steps are being proposed at this stage, rather than later, to asure that spending is kept within the initial targets.

In both houses, Democratic leaders described the Republican tax cut proposals as politically alluring siren's songs that would do the economy more harm than good.

Responding to Armstrong's allegation that the Senate Budget Committee proposal amounted to no more than "business as usual," Sen. Ernest F. Hollings (D-S.C.) the committee's acting chairman, said the government could "hardly do business at all" under the GOP counterproposal.

It would deprive poor people of needed services, said Hollings, and strip the economy of any "cushion" against inflation.

In the House, Majority Leader Jim Wright (D-Tex.) said the Republican proposal was tantamount to economic suicide and so severe in its domestic cuts that it would force an end to the food stamp program and even cutbacks in Social Security benefits.

But leaders of the Congressional Black Caucus, which wants more domestic spending than either the Budget committees or the Republicans are proposing, took a dim view of all the alternatives. It is only a question, said Rep. Parren J. Mitchell (D-Md.), of whether to "bleed to death or die quickly."

Both sides invoked the specter of deepening recession to bolster their arguments. Republicans contended that a business-oriented tax cut is needed to spur recovery through greater productivity, and Democrats argued that rising unemployment would siphon off tax revenues while adding to governmental costs, jeopardizing any chances that the budget will stay in balance through the next fiscal year.

According to many budget experts, the prospective 1981 budget can now be considered in balance only if it can count on $10 billion from the oil import fee that President Carter is imposing as part of his anti-inflation and energy conservation programs.

Carter contends that his budget proposal is balanced without the fee, but the House and Senate Budget committees' proposals for a tax cut reserve of roughly $10 billion for 1981 assume that the oil import money will be there.

However, some House and Senate members are trying to block the fee by legislation, and yesterday several House members, joined by consumer groups and an association of independent gasoline dealers, also sought to stop it in court.

U.S. District Court Judge Aubrey E. Robinson Jr. refused to grant their request immediately but scheduled a hearing Monday on the issue. The lawmakers, including Democratic liberals as well as Republican conservatives, contend that the fee, which the administration characterized as a conservation measure, is actually a 10-cent-a-gallon gasoline tax designed to raise enough revenue to balance Carter's budget. Taxes, they argue, can be imposed only by Congress.

At the same time, 28 senators, led by John H. Chafee (R-R.I.), introduced a resolution opposing another proposal that is keeping the Carter budget in ostensible balance: Carter's plan to raise $3.4 billion annually by withholding taxes that are now due once a year on savings interest and dividend income. Chafee contends that Carter's withholding tax proposal, which is subject to congressional approval, amounts to an involuntary "tax-free loan" by taxpayers to the government.

Meanwhile, House Democratic leaders indicated they will push ahead immediately after the House approves its budget resolution, perhaps today, to provide funds to keep the food stamp program in operation after June 1. The program will run out of money then unless Congress votes a supplementary appropriation, and the additional money has been held up pending action on the budget resolution.

Among the six Republicans who bolted their party's position on a tax cut in the House was Rep. John B. Anderson (R-Iii.), who is running as an independent for president. Washington-area legislators were generally divided along party lines in both houses, except for Sen. Charles Mc.C. Mathias (R-Md.), who voted against the Senate tax cut proposal. Sen. Harry F. Byrd jr. (Ind.Va.) voted for the tax cut.