Defense Secretary Caspar W. Weinberger yesterday was rebuked sharply by Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) for resisting a budget compromise, as leaders of both parties on the committee appealed once more to the White House for an accord.

Weinberger reportedly has urged President Reagan to bypass the budget process and fight for his program in individual appropriations bills. "Anyone who thinks that's the way to do it is living in ancient times," Domenici responded.

Clearly referring to Weinberger without mentioning his name, Domenici said the strategy advocated by Weinberger would not work, and vowed to continue working with both Democrats and Republicans to produce a budget.

"We must have a budget resolution, and I'll do everything in my power to do it," Domenici said, adding he hoped the White House would do the same.

Although the committee remained deadlocked, especially on taxes, a glimmer of hope arose when compromise-minded presidential aides asked for a meeting last night with Majority Leader Howard H. Baker Jr. (R-Tenn.) and Domenici in hopes of finding common ground for a budget agreement. The meeting lasted about two hours, and it was not known whether a compromise had been proposed.

Reagan appeared to remain adamant against major tax increases for the next two years, congressional sources said, but they indicated there might be some leeway on defense, which Weinberger has been successfully resisting thus far.

At the White House, presidential spokesman Larry Speakes continued to defend the president's budget, which includes a defense buildup of 10 percent after inflation, but also said the White House was "continuing to work with the Senate Budget Committee," which has whittled the defense increase down to 5 percent.

In what a Senate leadership source took as a potentially significant remark, Speakes said, "It is our hope we can move this defense budget figure into a range that is at least closer to the president's figure than this 5 percent that they're now acting on."

At a brief Budget Committee meeting, ranking Democrat Lawton Chiles (D-Fla.) joined Domenici in siding publicly with Office of Management and Budget Director David A. Stockman in Stockman's internecine battle with Weinberger over compromising with Congress on the budget.

In a bleak assessment that was quickly leaked to the press, Stockman told Reagan at a Cabinet meeting Monday that failure to compromise on the budget could produce staggering deficits for years to come and abort the economic recovery that is just starting.

Agreeing that failure to produce a budget could lead to economic "chaos," Chiles said he was "delighted" with the position Stockman has taken. There was irony in Chiles' remark, given the pummeling that Stockman was taking from Democrats a year or more ago for his handing of Reagan's budget.

But Chiles insisted that the Republicans would have to give more than they have on taxes if they're going to get a budget.

"It's going to take some reality on their side. Some, including the White House, want no revenues new taxes for 1984 and 1985 . . . but they don't have the votes," he said.

In pursuit of those votes, committee Republicans yesterday were exploring the possibility of a one-year budget that would require only nominal tax increases next year while assuming larger increases in the future to signal the prospect of declining deficits.

But, with Democrats insisting on immediate tax increases to help bring down deficits without further heavy cuts in domestic spending, it was not clear how the committee could approve such a plan and still retain the bipartisan alliance upon which it based its earlier decisions on spending.

The Republican leaders are in a bind because they want support from a majority of the 12 Republicans on the 22-member committee, which is proving difficult in light of shifting constituencies for key elements of the budget, including taxes, defense and domestic spending. Some say they believe that White House support for a compromise could be critical, as it was last year, in getting a majority of Republican votes.

Domenici was not the only Republican to vent frustration at the White House yesterday.

"They're not involved because they don't accept our defense mark number ," said committee member Dan Quayle (R-Ind.). "They're like a little kid playing marbles. If they don't win, they pick up their marbles and go home."