The Senate Demorcratic leadership moved to choke off a three week old Republican filibuster against the controversial labor law revision bill yesterday as President Carter reaffirmed his support for the union-backed legislation.

Senate Majority Leader Robert C. Byrd (D.W.Va.) filled the first in an expected series of motions to cut off the debate, setting the stage for filibuster ending votes tommorrow and Thursday.

The early cloture votes are expected to fail, but the bill's backers yesterday continued to express confidence that the talkathon will be broken soon. "certainly by the end of next week," according to Sen. Harrison A. Willaims (D.N.J.), the legisiation's chief sponsor.

Senate Minority Leader Howard Baker (R.Tenn.) appeared less certain about the outlook for the opposition. "I think it's up in the air," said Baker, a filibuster supporter.

Under Senate rules, 60 votes are needed to cut off debate. Some wavering senators have indicated they may vote to end the debate only after opposing cloture on the first few tries.

A quick cloture vote, however, will not automatically end the delay on the bill. Opponents have filed more than 400 amendments, which could take weeks to process.

However, supporters have signaled that some major "refinements" may be offered to make the bill less controversial and thus hasten final action on it.

The legislation, drafted jointly by the White House and organized labor, would set deadlines for union represenatation elections and stiffen penalties against employers who violate the law in an attempt to thwart union organizing and negotiating efforts. Opponents argue that the bill is a union "power grab" that would drive many small businesses into the ground. Proponents contend it merely puts teeth into existing laws guaranteeing workers the right to unionize.

In his second reafirmation of support for the legislation in less than a month, Carter said at a White House strategy session that the bill is "both needed and moderate . . . constructive for employers and employes."

Attending the meeting, along with Carter, Labor Secretary Ray Marshall, Byrd and Williams, was one Republican, Sen. Jacob K. Javits (N.Y.), a co sponsor of the bill.

Carter said the revisions were needed because there are "unwarranted delays in setting labor disputes" and inadequate penalties to ensure compliance with the law.

He noted that labor law revision legislation, a stronger version of the measure being filibustered in the Senate, plassed the House "overwhelmingly" last year, but conceded that it will take a "tough battle" to win Senate approval.