President Carter's bid for broad authority to reorganize the government made headway on two fronts yesterday, with a friendly Senate hearing and a promise of action on the House side of the Capitol.

The Senate Governmental Affairs Committee scheduled a vote on legislation restoring the Presidents reorganization powers for Feb. 23, after two hours of hearings produced a broad consensus of support. Republican senators questioned several details of the Carter proposal but only Sen. Lee Metcalf (D.-Mont.) indicated strong doubts about the basic authority Carter is seeking.

Meantime, House Government Operations Committee Chairman Jack Brooks (D.-Tex.), the major critic of the Carter bill, said after a meeting with the President that he would schedule hearings at an early but unspecified date.

"There's not going to be any difficulty about it," Brooks said after attending a meeting with Carter and Democratic congressional leaders.

Carter is seeking restoration of authority that allows a President to reorganize subcabinet agencies by plans that take effect automatically unless disapproved by one house of Congress within 60 days. The law was in effect from 1949 to 1973, but was allowed to lapse during the dispute over executive powers between President Nixon and Congress.

Brooks, who led the first to strip Nixon of that power, is objecting to giving it to Carter, and is proposing, instead, that reorganization plans take effect only, when affirmatively approved by both houses of Congress.

The essence of Brooks' argument was echoed yesterday by Metcalf, who said in a prepared statement that the Carter proposal called for "an unreasonable delegation of legislative power" and "will seriously upset the balance of power which we in Congress have so vigorously sought to achieve in recent years."

But Metcalf did not even bother to read the statement or question Bert Lance, the director of the Office of Management and Budget, who testified for the Carter bill.

All other committee members endorsed the basic principle of the legislation and focused their questions on relatively minor changes Carter is seeking in the old authority.

Sens. Charles H. Percy (R-Ill.) and Jacob K. Javits (R-N.Y.) questioned the need for a four-year extension rather than the two-year authority customary in the past. They sought assurances that Carter would not "swamp" Congress with reorganization plans if the statutory limit of one plan per 30 days was revoved, as Carter has asked.

They questioned Carter's desire to eliminate cost-savings estimates from the plans and his desire to include more than one subject per plan.

But the two Republicans appeared willing to accept Chairman Abraham A. Ribicoff's (D-Conn.) suggestion that these matters could be negotiated at the staff level before the Feb. 23 markup on the legislation.

The committee also seemed anxious to skirt the legal dispute over the constitutionality of the so-called "one-house veto" in the reorganization procedure.

Lance brought an option from Attorney General Griffin B. Bell arguing the constitutionality of the procedure, but that view was challenged by Antonin Scalia, an assistant attorney general in the Ford administration.

Meantime, Brooks had his first face-to-face meeting with Carter since he complained Friday that the bill Carter offered Congress that day "stands the Constitution on its head."

Taking a somewhat softer tone, Brooks said he promised the President that his committee will hold hearings on the bill "soon," but did not set a date.

Without withdrawing any of his objections to Carter's proposal, Brooks told reporters outside the White House that "we'll give everybody an opportunity to express their view, but if the majority support one program that's what it will be."