House and Senate leaders said yesterday that they will meet today to debate how deeply the administration's 1987 defense budget request must be slashed, after virtually abandoning hope of convincing President Reagan to raise taxes if he wants his request left intact.

"The time for missionary works ends Tuesday," Rep. William H. Gray III (D-Pa.), chairman of the House Budget Committee, said of the futile attempts thus far by his Senate counterpart, Sen. Pete V. Domenici (R-N.M.), to budge Reagan on taxes.

"We're not going to savage domestic programs any further and you can't get any more money for defense without breaking the deficit target, unless you raise more revenue," Gray said. "Pete [Domenici] has had a whole week to do the missionary work with the White House. I'm going to tell him that tomorrow and suggest we go ahead and try to agree on a figure on Wednesday."

Gray's strategy, according those involved in efforts to negotiate a compromise, is to take the lowest spending numbers from the budget resolutions passed by the House and Senate and split the difference when it comes to the Pentagon.

President Reagan requested $320 billion for defense budget authority -- the amount the Pentagon is authorized to spend -- in the fiscal year beginning Oct. 1. That would be $34 billion more than approved for 1986. The House voted to slash this amount to $285 billion, while the Senate agreed on $301 billion. Under Gray's strategy of splitting the difference, the Pentagon would receive $293 billion.

Reagan estimated the Pentagon actually will spend $274 billion in fiscal 1987, an estimate that Gray and others believe is $15 billion too low. Actual spending, rather than the budget authority side of the budget, will trigger cuts under the Gramm-Rudman-Hollings deficit reduction law. The cuts would be imposed automatically if the government forecasts that it will spend $144 billion more than it will take in during the fiscal year.

Domenici confirmed during a meeting of the American Stock Exchange that he has urged Reagan to reverse his longstanding opposition to tax increases in return for a congressional pledge to earmark most of the new government income for the Pentagon. Without tax hikes, Domenici said he told the White House, Congress will impose "draconian cuts, cuts substantially bigger than they [administration officials] were expecting two to three months ago."

Domenici said that he expects a White House reply this week. A senior White House official predicted that the answer to the New Mexico Republican will be, "Forget it."

"He's trying to put us in a quandary" by forcing a tax increase to pay for defense, the official said, adding: "What about cutting domestic spending? We're not getting into a box. It's not an either-or situation."

And Defense Secretary Caspar W. Weinberger said yesterday: "We have no doubt at all that a tax increase would not only hurt the economy, but would not help the nation's security. It would be applied to more domestic increases which, in turn, would be the justification for higher taxes in subsequent years."

Gray said that the administration is refusing to face the reality of three pressures that will require deep cuts in defense unless additional taxes are imposed: congressional refusal to cut domestic programs further; slower growth in the national economy than anticipated and lower inflation, meaning less tax revenue for the government; and Republican opposition in the House and Senate to tax increases if Reagan does not endorse them.

Gray said about 200 House Democrats have signed a letter declaring, "We reaffirm our strong opposition to any significant increase in the defense funding level over that adopted by the House."