The Republican-controlled Senate gave overwhelming bipartisan approval yesterday to far-reaching budget controls aimed at eliminating the deficit by 1991. The vote was 75 to 24.

As the Senate broke a week-long impasse over the measure, the Reagan administration acted to keep the government solvent for at least a week.

Together, the two actions brought the government -- at least temporarily -- back from the brink of the default that the Reagan administration had threatened to pressure Congress to pass the budget plan.

But the administration and the Senate appeared to lose leverage for prompt action on the budget plan by the Democratic-controlled House as that body balked at a Senate effort to extend the government's credit only through the end of next week. House Democratic leaders contended that the government has access, through the Federal Financing Bank, to sufficient funds to last until the end of the month. That gives the House more time to negotiate a compromise budget plan.

The balanced-budget measure was favored by a majority of senators from both parties. Sen. Edward M. Kennedy (D-Mass.) and 26 other Democrats abandoned their own leadership to join nearly all Republicans in a powerful demonstration of the mounting political force of the deficit issue.

"We are all crying 'fire' in the overcrowded theater of the federal deficit. We cannot continue to debate endlessly which fire extinguisher to use while the fire itself rages on," Kennedy said in a surprise endorsement of the GOP-drafted proposal.

The plan, spearheaded by Sens. Phil Gramm (R-Tex.), Warren B. Rudman (R-N.H.) and Ernest F. Hollings (D-S.C.) and embraced by the Senate GOP leadership and the White House, would set fixed deficit ceilings that would decline $36 billion a year from $180 billion this year to zero in fiscal 1991.

The president and Congress would be required to prepare budgets within these ceilings. If the deficit appeared likely to be exceeded at the start of a fiscal year, the president would be required to make across-the-board cuts in spending under guidelines established by Congress.

In order to win support of lawmakers restive over the plan's apparent transfer of powers from Congress to the White House, sponsors agreed to several modifications, including a requirement that cuts be uniform in conformity with priorities established in appropriations bills.

Previous language was ambiguous, prompting Democratic charges of a massive transfer of power to the president. Sen. Carl Levin (D-Mich.) said his proposal, accepted by the Republicans after intense negotiations, means "the president cannot pick and choose . . . everybody's ox is going to get gored."

In addition, while the politically popular Social Security program would be shielded from cuts, other benefit programs not affected by cost-of-living adjustment cutbacks would be subject to reductions. Also accepted were changes aimed at relieving restrictions during a recession and assuring that agricultural programs would be subject to the cuts.

Some senators, however, remained skeptical that the plan would work as designed. It will "come back to haunt" Congress, Minority Leader Robert C. Byrd (D-W.Va.) said.

It is a "tribute to the failure of Reaganomics" and a "travesty" that will inflict more suffering on those who have already borne the burden of Reagan budget cuts, Sen. Gary Hart (D-Colo.) said. But Kennedy, a possible rival to Hart for the 1988 Democratic presidential nomination, said it would impose some restraint on the administration's defense-spending "spree."

Democrats supported the plan only after a Democratic leadership alternative was defeated. It would have required cuts next year and balanced the budget, a year earlier than the Gramm-Rudman-Hollings plan. It would also have made it easier to impose tax increases as well as spending cuts to comply with the deficit targets. It also sought to bar Reagan from vetoes of congressional spending cuts simply as a way to use his new power to make his own cuts instead.

Also rejected was a Democratic proposal that would have forced the spending cuts to take effect before next year's congressional elections. Democrats had complained that the deficit was allowed to be so high the first two years so that Republicans could get through the campaign season without making painful budget choices.

While 27 Democrats of both liberal and conservative outlook broke rank with their leaders on the budget plan, only four Republicans defected from their party.

As Congress broke off early so Democrats could attend a fund-raising gala, the Senate was still working on refinements to the proposal, which will be added to a long-term debt ceiling extension. That would extend the current $1.824 trillion debt to $2.078 trillion, enough to last a year. This bill, or another short-term extension, will have to be passed when the Federal Financing Bank credit runs out.

The Senate expects to complete action on the long-term measure today and send it to conference with the House for compromise talks on the balanced budget aspects before the new credit authority runs out. One White House official said yesterday afternoon that he believed the balanced budget plan could well die in a bitter conference.

But it apeared the administration may have a more difficult time in the future using debt deadlines as leverage.

"The next time the Treasury comes around crying wolf, remember tonight," Sen. William L. Armstrong (R-Colo.) said. "It wasn't true."