Senate Majority Leader Robert C. water down the administration's labor Byrd (D-W.Va.) moved yesterday to law revision package as the Senate, for the second day in a row, refused to shut off debate on the controversial union-backed bill.

The concessions caused grumbling among labor lobbyists hovering outside the Senate chamber but failed to mollify filibuster leaders, who promised to keep on talking.

Backers of the legislation, which would generally make it easier for workers to organize and win contracts, had not expected to break the 12-day filibuster on the second try and took cheer from the fact that the 49-to-41 vote was an improvement over Wednesday's 42-to-47 vote. They took even more heart from a 51-to-37 vote against sending the measure back to the Senate Human Resources Committee.

But the timing of Byrd's proposed revisions, while expected at some stage in the long fight over the labor bill, raised questions about whether debate-ending cloture could be achieved without some substantial modification to win over wavering senators.

Some Senate and labor sources insisted the votes were there to do it, attributing Byrd's move to making life easier for senators who want to vote for cloture but are under heavy pressure to oppose it, and to a long-range strategy for dealing with the nearly 500 amendments to the bill that face that face the Senate even if cloture is invoked.

Byrd's revisions would extend the proposed time schedules for holding union representation elections and limit proposed union access to workers when union representatives go on company property. The revisions are a response to so-called "captive audience" arguments against unionization by employers.

The revisions would also provide for mandatory reinstatement of federal contracts canceled because of labor law violations if the employer ceases to violate the law and modify the so-called "make-whole" remedy by which workers would get wage increases if their employers illegally refuse to bargain for a contract.

Also incorporated in the proposed revisions was a previously offered Byred amendment to freeze the National Labor Relations Board's jurisdiction over small businesses, thus assuring that no additional small operators would be brought under federal labor laws and subjected to provisions of the proposed legislation.

Byrd said the changes would assure that the bill is "evenhanded and fair," especially to small business operators, hundreds of whom rallied against the bill on the Capitol steps earlier in the day.

However, the proposals were dismissed as insufficient bythe bill's opponents, who said the concessions would not derail the filibuster. They will require "careful examination," said Senate Minority Leader Howard H. Baker (R-Tenn.), "and I must say in all candor . . . it will take a while."

Sen. Orrin Hatch (R-Utah), the filibuster leader, said the bill was basically the same, only with "some very tricky . . . nuances" added. It would still provide for "quickie elections" for union representation and other changes that fail to meet opponents' objections that the bill's one-sided in favor of organized labor.

Sen. Jacob K. Javits (R-N.Y.), a supporter of the bill, responded that Byrd's proposed changes show that the bill's backers are not "cast in concrete" on the issue.

There will be no cloture votes today or Monday but Byrd said another attempt to break the filibuster will be made Tuesday, with another vote to follow on Wednesday if, as expected, Tuesday's vote falls short.

The administration was understood to support Byrd's proposed modifications, but some labor lobbyists expressed displeasure at the timing and indicated they thought his move was unnecessary.