The fiscal 1987 budget approved by the Democratic-controlled House Budget Committee drew fire from Republicans yesterday, as Senate GOP leaders charged that it would damage national defense and President Reagan's budget director said it added "insult to the injury" inflicted by the Senate.

But House Budget Committee Chairman William H. Gray III (D-Pa.) predicted that the budget resolution will pass the House, with or without the bipartisan support that Democratic leaders have been seeking for tax increases that are opposed by the Reagan administration.

Gray criticized Senate Majority Leader Robert J. Dole (R-Kan.) for saying he would "break up" a House-Senate conference on the budget if it failed to produce a defense-spending compromise satisfactory to the president.

The budgets approved Thursday by the House committee and last week by the Senate are "not that far off," even in defense spending allocations, Gray said, adding that he was "appalled" that Dole would scuttle a budget agreement rather than compromise on defense spending.

Both versions of the budget resolution would raise Reagan's proposed revenue increases for next fiscal year from $6 billion to $13.2 billion, with the Senate using the revenue to increase defense spending, while the House committee would use it for deficit reduction beyond what is required by the Gramm-Rudman-Hollings budget-control law.

Both plans also basically freeze nondefense spending, with some differences over how the money would be allocated within domestic accounts.

They differ primarily over defense spending authority. The Senate would increase the military budget of $287 billion to $301 billion; the House would cut it to $285 billion. Reagan requested $320 billion.

In a statement yesterday, Office of Management and Budget Director James C. Miller III made it clear that he considers the House plan worse than the Senate plan that the administration criticized last week. "The [House committee's] budget resolution . . . adds insult to the injury already occurring in the budget process," Miller said in what an aide described as a reference to the Senate budget. Miller vowed to seek changes in the House, in conference committee and "in subsequent legislation," an apparent reference to tax and spending measures later this year.

Dole and Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) also weighed in against the House defense spending plan, which Dole characterized as "irresponsible and totally unrealistic."

"If there's anybody over there [in the House] that really believes that you can provide for the national defense with those numbers, then I don't know where they are getting their information," Domenici said.

Rep. Delbert L. Latta (Ohio), ranking Republican on the House Budget Committee, attacked the budget's tax provisions as a "phony scheme" under which revenues would be designated for deficit reduction but could be used for spending.

Latta's comments, coupled with the virtual party-line vote in the House committee on the budget, underscored the difficulties that Democratic leaders are expected to have in getting bipartisan support for raising taxes. All Republicans voted to strip extra "deficit reduction" taxes out of the budget, and only one, Rep. Vin Weber (Minn.), voted for the budget on final passage.

The Democratic leaders, fearing their party will be attacked once again by Reagan for "tax-and-spend" excesses if they vote for tax increases, have said they will not support the increase unless Republicans go along.

But Gray said yesterday that he expects them to support the budget on the House floor, while insisting on GOP support before actual tax legislation is voted on. The budget resolution, while calling for tax increases, does not require the House Ways and Means Committee to propose such legislation.