Senate Majority Leader Robert C. Byrd (D-W. Va.) said yesterday that, starting June 7, cloture votes will be taken daily in an effort to cut off the filibuster against the administration's labor law revision bill.

As the debate entered its second week, Byrd told reporters he would file the first anti-filibuster petition after the Senate returns June 5 from a week long Memorial Day recess.

Administration and organized labor lobbyists have conceded they will lose the first cloture vote, which requires 60 senators to vote to limit further debate on a bill.

Victor Kamber, coordinator of the AFL-CIO's campaign on behalf of the controversial measure, said yesterday that cloture is seen as possible on the second vote but more likely sometime the following week. Opponents have said they will resist cloture as long as possible and, if their resistence fails then delay action on the bill by bringing up hundreds of amendments.

The filibuster is aimed at forcing the Senate Democratic leadership to withdraw the bill. The leadership has said it will not do so.

The bill, which has provoked a battle between labor and business lobbyists, would set deadlines for union representation elections and stiffen penalties for employers who violate labor laws to thwart organizing drives and collective bargaining efforts. Among its provisions are time-and-one-half back pay for workers fired illegally for trying to organize a union, loss of federal contracts for "willful" violators of labor laws, and compensation of workers for wages lost during illegal efforts to delay a contract settlement.