The Republican-controlled Senate, frustrated by failure to win concessions from the White House and Democratic-run House, ended a monthlong stall yesterday and began considering a budget blueprint for next year.

It did so with a mixture of impatience, dread and suspense, forced to act by deadlines imposed by the Gramm-Rudman-Hollings budget-control law, but with little or no assurance of where the ordeal will lead.

"We have to face a budget vote whether we like it or not," said Senate Budget Committee Chairman Pete V. Domenici (R-N.M.). Just getting it to the Senate floor was "like trying to jump-start a car on a winter day," observed Sen. Lawton Chiles (D-Fla.), ranking Democrat on the panel.

"The question is whether or not we have the votes" to pass anything, said Majority Leader Robert J. Dole (R-Kan.).

The Senate GOP leadership had hoped to convince the White House to compromise on key tax and spending issues and to get the House to move simultaneously with the Senate on the budget, but failed on both counts.

So, six days after the April 15 deadline that Congress had imposed on itself for final action on the fiscal 1987 budget, Dole brought up a controversial Domenici-Chiles plan approved last month by a bipartisan majority of the Budget Committee.

The committee draft defied President Reagan by proposing to raise taxes by $12.5 billion more than he wanted while rejecting many of his proposals for domestic program cutbacks and slashing $25 billion off his defense spending request. The White House has denounced the committee plan, and House leaders have refused to develop a plan of their own until the Senate finishes its work.

Dole brought up the budget after a meeting with House leaders during which Democrats indicated they might consider tax increases if the Senate proposes it and House Republicans go along.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) "no longer insisted that the president had to be first" in proposing a tax increase, Chiles said.

But House Minority Leader Robert H. Michel (R-Ill.) saw it another way, contending that the Democrats now wanted him "on board" before they would move on taxes. "That's an unreasonable request to make of me," Michel said.

A Democratic leadership aide said that, unless Reagan supports a tax increase, it would have to have "bicameral and bipartisan" support to gain House Democratic approval.

"It would have to originate in the Republican Senate and have Republican support in the House," one aide said, conceding that this might be as difficult, if not more difficult, than obtaining Reagan's backing.

House Democratic leaders remained adamant againt moving "in tandem" with the Senate on a budget, as Dole and Michel had requested, but indicated that they would be ready for House action "within 72 hours" of Senate approval of its version of the budget.

In a statement issued after the meeting, Dole and Michel said, "It is still our hope and expectation that we can produce a bipartisan and bicameral package that meets our mutual concerns on requirements on taxes, defense and spending cuts."

The Senate budget plan includes $5.9 billion in new revenue proposed by Reagan, including an extension of the 16-cents-a-pack cigarette tax already law, along with another $12.5 billion in unspecified revenue increases that Reagan does not want.

It would also cut Reagan's request for defense-spending authority from $320 billion to $295 billion, hardly enough to offset inflation. Reagan's request amounted to an increase of 8 percent above inflation.

It included nondefense spending cuts of about $17 billion, partly offset by $3 billion in increases for some programs, with virtually none of the program terminations sought by Reagan. The net domestic savings were only about half of what Reagan proposed.

Dole, noting that 24 of the Senate's 53 Republicans are on record as opposing the committee plan, reiterated that he thinks it should be modified to include more for defense, less for domestic programs and a smaller tax increase.

He said at a luncheon meeting with reporters that domestic spending could be cut $5 billion to $6 billion more by incorporating cuts and program terminations approved last year by the Senate.