Only a day after approving a plan to balance the federal budget within six years, the Senate voted overwhelmingly yesterday against proposals for raising taxes and cutting defense and Social Security spending to help reach the goals.

"What is Congress prepared to do after this great day? The answer is nothing," said Sen. Bill Bradley (D-N.J.), who offered the tax and defense proposals, only partly tongue-in-cheek, to demonstrate the difficulties Congress will have meeting its own targets.

After a day of action on mop-up amendments to the balanced-budget bill, the Senate approved it, 51 to 37, as part of a 12-month debt-ceiling extension raising the borrowing limit from $1.824 trillion to $2.078 trillion.

Among major modifications were provisions limiting the president's discretion in ordering spending cuts and subjecting some defense weaponry contracts to the cutback requirements.

Contracts could be affected if cuts did not violate legal requirements or cost more in penalties than was saved. Disputes remained, however, about vulnerability of some major programs, such as Medicaid and Aid to Families with Dependent Children, to the cutback requirements.

Sen. Sam Nunn (Ga.), ranking Democrat on the Senate Armed Services Committee, said defense cuts under the plan would be "very serious" although justifiable in light of the need to cut deficits. If the constraints had been applied to the fiscal 1985 budget, the defense outlay cut would have amounted to $13 billion, he said.

The debt measure and balanced-budget proposal now goes to a conference with the House, which Senate Budget Committee Pete V. Domenici (R-N.M.) said he expects to be "very tough." Domenici said the conference will probably begin Tuesday or Wednesday.

As the Senate finished the bill, House Democrats struggled to devise counter-proposals for the conference, including provisions to strengthen congressional control over deficit reductions.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said he believed that some kind of balanced-budget legislation would pass but continued to criticize the Senate measure.

House Democratic sources said they would not be surprised if the House approves a GOP proposal to instruct House conferees to accept the Senate plan when conferees are appointed, presumably today.

In the Senate, Bradley's tax proposal -- designed to raise $70 billion over five years by increasing the gasoline tax from 9 to 27 cents a gallon -- was rejected, 89 to 9.

His proposal to cut defense spending by 5 percent to come within the fiscal 1987 target in the balanced-budget plan died, 89 to 7.

The Senate also rejected, 71 to 27, a proposal from Sen. David L. Boren (D-Okla.) to include Social Security in programs subject to mandatory across-the-board cuts if deficit targets are exceeded.

Bradley's skepticism was reflected in an acerbic assertion by Sen. Daniel Patrick Moynihan (D-N.Y.) that cuts promised in domestic and defense programs are so deep that they amount to a "triumph of reaction at home and isolation abroad." He added: "A majority of Democrats agreed to dismantle the domestic policies of Franklin D. Roosevelt, in return for a majority of Republicans agreeing to dismantle the defense policies of Ronald Reagan."

The balanced-budget plan, as approved Wednesday by a vote of 75 to 24, would require the president to make proportional cuts in defense and domestic spending, except for Social Security, if deficits exceed fixed targets set in the legislation. The targets are aimed at reducing deficits from $180 billion this year to zero by fiscal 1991.

Taxes were not included, but many lawmakers have privately argued that increases would be required to avoid unpalatable spending cuts.

The proposal was tacked onto an urgent debt-ceiling extension that the Senate hoped to use as leverage to force approval of the budget-balancing rules from a skeptical House. But that strategy was foiled when the Reagan administration found ways to keep the government solvent without extending the limit.

This involved a swap of Treasury Department securities for others held by the government's Federal Financing Bank that are not subject to the debt limit. The effect was to lower the official level of debt and thus allow the Treasury to borrow more.

The maneuver drew the wrath of Senate Majority Leader Robert J. Dole (R-Kan.), who charged yesterday that the Treasury didn't have "guts" enough to join the Senate in debt-ceiling brinksmanship to force approval of the budget plan.

"What they've done is give the House plenty of time to try and kill the package . . . . [House members] should have been kept under pressure for a few days," said Dole.

But administration officials said Dole had been warned that the Treasury would resort to financing bank authority if the government was on the verge of default and that there was no other way of holding off the potential default.

Dole knew, officials said, that the administration did not intend to allow a default -- which would have potentially wide international and national ramifications -- simply to help the Republicans apply political pressure.

Dole has periodically crossed swords with the administration, especially when its actions have the effect of helping the Democratic-controlled House out of a box, as the debt-extension maneuver did. But rarely has he been angrier, at least in public.

"I think they're going to have a big credibility problem when they send their next 'daily tremble' letter up here," he said.

Paul S. Trible Jr. (R-Va.) was the only Maryland or Virginia senator voting to increase the debt limit.