The Senate overwhelmingly approved early today a modified bipartisan tax-and-spending plan for next year, breaking a long, stubborn standoff over how to meet the Gramm-Rudman-Hollings deficit-reduction targets.

After winning preliminary approval in both Republican and Democratic party caucuses, the $1 trillion budget plan was approved by the Senate in back-to-back votes of 66 to 29 and 70 to 25.

Passage of the plan by the Republican-controlled Senate paves the way for the Democratic-run House to begin formal work on its version of the budget, possibly next week. House leaders were waiting for the Senate to act first, but promised budget panel approval of a House plan within 72 hours of Senate action.

The Senate plan included about $13 billion in new taxes, roughly halfway between the $6 billion proposed by President Reagan and the $18.7 billion recommended by the Budget Committee.

It also called for $301 billion in defense spending authority, or $19 billion less than Reagan requested and $6 billion more than the budget panel approved. This was at least enough to cover the cost of inflation, far short of the administration's request for an increase of 8 percent above inflation.

There was no immediate reaction from the presidential party en route to Japan, but Senate Majority Leader Robert J. Dole (R-Kan.) said he thought the president would be relieved at passage of the budget although disappointed by specific tax and spending decisions.

The plan also included some additional domestic program cuts, including termination of about 12 programs, mostly small ones that had little political support. The Budget Committee had voted to kill only three programs, one of which -- the Work Incentive Program providing job-related aid to welfare recipients -- was restored by the Senate.

In all, the plan contained $8.7 billion in new domestic spending cuts, partly offset by $1.5 billion in additional domestic funding. Officials said $5.6 billion of the reduced domestic spending resulted from re-estimates of cost, including lower cost-of-living increases for pension programs because of reduced inflation estimates.

Cost-of-living increases would be held to 2 percent and pay increases for federal workers would be kept consistent with inflation.

A majority of both Republicans and Democrats voted for the modified plan on the critical first vote. Republicans voted 38 to 13 for the plan; Democrats voted 28 to 16.

All Washington area senators supported the plan, except for Sen. Paul S. Sarbanes (D-Md.), who opposed it in the preliminary vote but switched his support for final passage.

The day had begun on a bitter, confrontational note as Dole accused House Democrats of trying to "trap" Senate Republicans into leading the way toward a controversial election-year tax increase.

House Democrats responded in kind, charging that Dole, stymied in trying to reconcile conflicting pressures within his own party and hampered by running for president while leading the Senate, was picking on them because he is "stuck and needs a place to hide."

Despite the partisan theatrics, efforts to work out a Senate budget compromise continued throughout the day on several fronts, resulting in the caucuses on a revamped bipartisan plan from Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) and Sen. Lawton Chiles (D-Fla.), ranking Democrat on the budget panel.

A previous Domenici-Chiles plan had been approved by a majority of both parties on the Budget Committee but was opposed by Reagan, Dole and two dozen Senate GOP conservatives, all of whom complained that it contained too large a tax increase and too small an increase in defense spending.

Dole, who had been meeting all day with Senate Republicans and administration officials to work out a compromise acceptable to the president, said he would support the revised plan even though it did not go as far toward meeting White House objections as the alternative that Dole pushed.

Dole, in telephone contact with the presidential party in East Asia, was told by White House chief of staff Donald T. Regan that the president would indicate "some disappointment" over the outcome, but would say he "appreciates the fact that the Senate met its responsibilities."

It was not a "flat-out endorsement," Dole said, noting that the president still wanted more for defense, less for domestic programs and a smaller tax increase.

Dole had insisted on support of at least a majority of Republicans for any compromise, complaining that the earlier Budget Committee draft lacked such a majority. Sources said the caucus split 33 to 12 in favor of the revised plan.

Domenici predicted that passage of the plan would ensure Congress would meet the Gramm-Rudman-Hollings deficit target of $144 billion for next year, thereby avoiding across-the-board spending cuts that would be required if the deficit target was missed. Without its passage, he added, chances of automatic cutbacks were extremely strong.

Earlier in the day, partisan rancor had flared as Dole and House Budget Committee Chairman William H. Gray III (D-Pa.) exchanged recriminations over House and Senate motives in their budget strategies over the last few weeks.

In what appeared to be one of a complicated series of maneuvers to build pressure for a compromise, Dole angrily waved a copy of what he described as a "House Democratic budget," describing it as "smoking gun" evidence that House Democrats were interested only in playing politics by trying to isolate Senate Republicans as the only champions of a tax increase.

He said he would not ask the Senate to support a budget containing tax increases until House Democratic leaders clarified their intentions. "We've been had . . . . It seems to be that all bets are off," he said.

The Democratic budget to which Dole referred was a draft cited by House Majority Leader James C. Wright Jr. (D-Tex.) earlier this week as the one House Democrats were prepared to take to the the House floor after the Senate completed action on its version. It would reach the $144 billion deficit target of Gramm-Rudman-Hollings without raising taxes, largely through much larger defense spending cutbacks than the Senate wants.

However, Wright and other House leaders later characterized it as only one of several options under consideration by House Democrats, and Gray described it yesterday as an "out-of-date House Budget Committee staff working paper."

Said Gray: "Sen. Dole is frustrated. He won't support his budget committee chairman Domenici and he can't support his president. It's part of the problem of being both Senate majority leader and a presidential candidate. So he's struck and he needs a place to hide. Apparently he thinks he can hide behind an out-of-date House Budget Committee staff working paper."