Budget director James C. Miller III said yesterday the Reagan administration cannot support a proposed budget compromise from the Republican-controlled Senate that calls for tax increases to finance extra spending for defense and domestic programs.

Miller, head of the Office of Management and Budget, warned that it may be "a long hot summer . . . into the fall" before the fiscal 1987 budget controversy is resolved.

The rejection, in line with earlier administration opposition to tax increases and defense spending cutbacks, came as Democratic-led House budget negotiators prepared to respond today to the offer that Senate bargainers laid on the table last Friday.

While indicating interest in the proposal, House Democrats expressed reservations on several counts, including fears that President Reagan would veto any tax increase and Congress would be unable to override the veto.

The Senate plan, offered by Budget Committee Chairman Pete V. Domenici (R-N.M.) and ranking Democrat Lawton Chiles (Fla.), would tie some extra spending for defense and domestic programs to congressional passage and presidential acceptance of tax increases amounting to $47 billion over three years, starting with $7.3 billion next year.

In a letter to Domenici, Miller renewed the administration's proposal that Congress rely on user fees and sale of government assets instead of tax increases to meet revenue targets in the budget.

He said $14 billion could be raised in this way over three years, coupled with $15 billion in spending cuts -- all of which was in the president's budget but rejected by the House and Senate in adopting their versions of the budget earlier this year.

Expanded asset sales, including selling off more government loan portfolios, was proposed informally by the administration last week to Domenici and Chiles and firmly rejected by the two senators.

Miller, at a news briefing, denied trying to "torpedo" congressional passage of a budget, saying the administration wants to see Congress pass a budget but also feels it would be possible to get by without one.

He also said the administration would be willing to consider making relatively small cuts in defense spending as a result of lower inflation but ruled out larger cuts that Congress wants.

On deficit projections, he said the 1986 fiscal year ending Sept. 30 appears worse than originally projected, but said fiscal 1987 is appearing brighter than it did when Reagan submitted that budget in February. He declined to give figures, however.