President Reagan is unwilling to support tax increases to finance more spending for defense, his spokesman said yesterday in response to a taxes-for-defense proposal from the Republican chairman of the Senate Budget Committee.

The comment by presidential spokesman Larry Speakes appeared to dim further the flickering prospects for a speedy congressional compromise on the fiscal 1987 budget to avoid big, across-the-board spending cuts this fall under the new Gramm-Rudman-Hollings budget-control law.

House-Senate budget conferees made substantial progress in ironing out differences over domestic spending in a day-long bargaining session yesterday, reaching tentative agreement on a 3 percent pay increase for federal civilian and military employes next year.

But as the conferees prepared to close in on the key issues of defense and taxes today, they indicated deepening pessimism about prospects for a settlement that would keep the deficit under the $144 billion Gramm-Rudman-Hollings ceiling for next year, so long as Reagan holds firm against tax increases.

Several conferees said changing economic conditions point to a deficit of at least $10 billion more than was anticipated when House and Senate budget resolutions were adopted earlier this year, meaning that if the target is to be met, Congress will have to cut spending or raise taxes more than was originally proposed.

House conferee Marvin Leath (D-Tex.) said the conferees are facing an "absolute prescription for disaster" because Reagan will not support tax increases and House Democrats are insisting on presidential support before embracing them. This could lead to a "contrived budget" that would meet the targets on paper only, inviting across-the-board spending cuts when the real deficit numbers become known in late summer. On the other hand, Leath added, "I don't know how you even get a contrived budget."

Rep. James C. Slattery (D-Kan.), another conferee, speculated that the budget conference might suspend until the tax-overhaul bill is worked out, in hopes that additional revenue will materialize there.

Despite Speakes' apparent rejection of tax increases on Reagan's behalf, Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) refused to give up. Asked about Speakes' comments, Domenici said he was still awaiting a response from White House chief of staff Donald T. Regan, with whom he discussed the taxes-for-defense proposal on Friday.

Domenici indicated he would call Regan to ascertain the president's position if Regan had not called him. "We're not going to wait around . . . . I think tomorrow is about right," he said. House Budget Committee Chairman William H. Gray III (D-Pa.) agreed it was time to move on defense and taxes.

Domenici suggested to Regan on Friday, and reiterated in a speech Monday, that most of the proposed tax increase of about $45 billion over three years be earmarked for defense, bringing the Pentagon's budget within reach of the Senate's defense spending proposal. The Senate had proposed $301 billion in new military spending authority, roughly halfway between the $320 billion sought by Reagan and the $285 billion approved by the House. Without a go-ahead on taxes, Domenici warned, Congress will impose "draconian cuts, cuts substantially bigger than they administration officials were expecting two to three months ago."

But Speakes said the president "does not want to raise taxes in order to finance the defense increase." And House Majority Leader James C. Wright Jr. (D-Tex.) indicated that the House might not go along in any case.

While agreeing tentatively to allow room in the budget for a 3 percent government pay raise (the House had proposed 3 percent, the Senate 2 percent), the conferees went along with a Senate proposal to make federal agencies absorb much of the cost by cutting other spending. Civilian agencies would have to absorb half the cost, the Pentagon one-third.