President Reagan's budget priorities came under a sharp, bipartisan assault yesterday as key members of the Senate Budget Committee called for higher taxes, lower defense spending or a combination of both to meet the $144 billion deficit target set for next year by the new Gramm-Rudman-Hollings balanced-budget law.

Voicing publicly what he said has been his private advice to the administration, Sen. Pete V. Domenici (R-N.M.), the committee chairman, opened the first hearing on the fiscal 1987 budget with a plea for negotiations leading to an overall package that he said must include "a revenue component."

"I think taxes can be the glue that binds the package together," Domenici said.

On the House side, Democratic leaders, including Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), accused the president of being unwilling to compromise on the budget and indicated that his proposal will get a long, hard look by the Democratic majority.

House Budget Committee Chairman William H. Gray III (D-Pa.) contended that Reagan's proposal underestimated actual defense outlays by $15 billion, putting the overall budget above the $144 billion deficit tar- get.

At the Senate Budget Committee hearing, as Office of Management and Budget Director James C. Miller III listened, other senators joined Domenici in calling for additional revenues or in dismissing Reagan's request for a steep rise in defense spending coupled with cuts in domestic programs.

"I don't see how we can get out of this without revenues," said Sen. Ernest F. Hollings (D-S.C.), one of the chief sponsors of the balanced-budget law.

"Do you think we're really going to seriously negotiate over savaging these programs for education, health and others while increasing foreign aid by one-third and defense by 38 percent?" Sen. J. Bennett Johnston (D-La.) asked Miller. "That's just not going to happen, and that's no way to start a conversation."

Sen. Charles E. Grassley (R-Iowa), one of 19 GOP senators seeking reelection this year, said he was willing to go along "at least initially" with the administration's opposition to a tax increase to meet the deficit target.

Taking aim at Reagan's defense spending proposals, Grassley said, "The best way to avoid a tax increase is not to ask for defense growth before the Department of Defense can spend what it has been given."

In his testimony, Miller hewed strictly to the administration line, warning that a tax increase to reduce the deficit could jeopardize economic growth, and defending the defense spending proposals as "consistent with what the country needs in order to provide for our national security."

On a related matter, Reagan told reporters yesterday he was "willing to look at" an oil-import fee, but only if the money it raised was used to pay for restoration of tax benefits in the House-passed tax-revision bill.

Miller, on the Hill, confirmed Reagan's statement, and Senate Finance Committee Chairman Bob Packwood (R-Ore.) said it increases the chances that he will put an oil fee in the tax-overhaul bill he is preparing for committee consideration.

However, Senate Majority Leader Robert J. Dole (R-Kan.) and Domenici said they would like to use the revenue from an oil import fee -- about $12 billion a year for a $5 a barrel fee -- to reduce the deficit.

Dole, who was speaking at the White House, said he opposed using the fee "to ease things on the tax-reform side."

In his remarks on the budget, O'Neill referred to Reagan's 1981 budget, which cut taxes and raised Pentagon spending, and said the country is now being hit by "the terrible consequences of that budget."

"Today we received the Boomerang Budget, the one that comes back to hit you," he said.

He said that in the spirit of Reagan's offer to work with him, "I intend to do everything in my power to ensure that his budget receives a fair and full hearing . . . . The president deserves his day in court and he will get it . . . . I want to help him inform the American people how much it costs to go to Tokyo for lunch."

The latter phrase was a reference to Reagan's State of the Union call for a "space plane" that could fly to Tokyo in two hours.

House Majority Leader James C. Wright Jr. (D-Tex.) scoffed at Reagan's offer of cooperation with the Democrats.

"That gesture was only window-dressing," he said. "He has no interest in compromising, he has no give -- he is rigid and inflexible. We met with him and his advisers two years ago and worked out a tax bill and then he hit us over the head with it all year in 1984. It wasn't a Democratic tax bill, it was a bipartisan bill."

Gray said he was "surprised" that the president's proposal underestimated actual defense outlays by about $15 billion, which would put it over the Gramm-Rudman-Hollings deficit target of $144 billion and could trigger the across-the-board "sequestration" procedure to bring the budget in line.

"The president shouldn't want sequestration because it will drastically cut defense spending," he said.

"I have a problem with this proposal," he said. "I'm for a strong defense but we have to pay for it. We're doing it on a credit card now. This is a continuation of the fiscal policies that gave us this debt in the first place."

Gray said, however, that the budget proposal was not already "dead" as some critics contend and predicted that there would be a vote on it.

"I think it's legitimate to look at the budget carefully, point by point, and have a vote on it," he said. "We won't have roads, mass transit, housing, job training, education or farm programs. He'll have a tough time selling this budget on the Hill. I don't know if it will pass the House, but I want to hear his pitch."

The House Budget Committee has scheduled field hearings next week, beginning in Chicago on Monday, then the Boston area, Tallahassee, Dallas and winding up in San Francisco on Friday.