Legislation to force a balanced budget over the next six years, which Republicans are trying to tack onto an urgently needed debt-ceiling extension, stalled in the Senate yesterday despite an endorsement from President Reagan and his plea for prompt action.

Democrats and Sen. Lowell P. Weicker Jr. (R-Conn.) threatened filibusters against the balanced-budget measure, prompting Senate Majority Leader Robert J. Dole (R-Kan.) to schedule sessions today and Sunday to break the impasse.

Resisting Democratic pressure for a brief extension of Monday's debt-ceiling deadline to allow more time for study of the balanced-budget proposal, Dole said the delay would only give time for opposition to mount. He hinted at hardball tactics to force a swift vote.

"The longer something hangs around here, the staler it gets . . . . People start reading it," Dole said.

"With checks coming back without being honored, we'll see who blinks first in the Senate," he added later, referring to the government's need for new borrowing authority to pay its bills after Monday.

Minority Leader Robert C. Byrd (D-W.Va.) responded that Democrats will not be forced into precipitous action on something that could have far-reaching implications for the economy and social welfare programs.

Momentum behind the balanced-budget proposal, which had built to a high pitch late Thursday, faded as the measure hit the Senate floor, where Democrats, in an apparent stall for time, characterized it as everything from a "pig in a poke" to a "sword of Damocles" to "Armageddon" for the country.

"We're not prepared to bring the sword of Damocles down on the poor, the young, the old and on all the defense and domestic programs," Byrd said.

Sen. J. Bennett Johnston (D-La.) was even more acerbic. "I believe this piece of legislation is the most far-reaching, the most horrendous, the most damaging to the constitutional process, the most extreme piece of legislation that I have seen in my 12 years in the Senate. I think it's Armageddon," he said

Joining them was Republican Weicker, who called it a "legislative substitute for the guts we don't have to do what needs to be done."

The proposal, drafted by Sens. Phil Gramm (R-Tex.), Warren B. Rudman (R-N.H.) and Ernest F. Hollings (D-S.C.), sets fixed limits for deficits, declining from $180 billion in fiscal 1986 to zero by fiscal 1991.

Both the White House and Congress would be required to submit budgets within those limits. If it appears at the start of a fiscal year that the limits will be exceeded, the president would be required to cut spending across-the-board in theoretically uniform amounts from discretionary programs and cost-of-living adjustments for entitlements. Only Social Security would be exempt.

Reagan endorsed the proposal early yesterday after the administration forced several modifications, mostly aimed at protecting defense spending, which could be cut substantially if automatic cutbacks become necessary.

"This legislation will impose the discipline we now lack by locking us into a spending reduction plan," the president said.

But he added several stipulations, including an insistence that Social Security be kept exempt from cutbacks and that "previous commitments on defense" be honored.

He said the plan "attacks budget deficits the right way, not by raising taxes but by restraining spending." However, many lawmakers, Republicans and Democrats, are saying privately that the specter of more deep, across-the-board spending cuts could create a more favorable climate for tax increases.

The dispute over implications for taxes was typical of disagreements among lawmakers yesterday about the political and fiscal fallout of the plan.

Defense was another example. Several House Democratic leaders contended it could be a wedge to force defense spending cutbacks as they welcomed the plan Thursday night as a basis for bargaining. But the Center on Budget and Policy Priorities argued yesterday that defense would not be subject to the same degree of reduction as most domestic programs.

There was also dispute over whether presidential powers would be expanded at the expense of congressional prerogatives.