Majority leader Robert C. Byrd (D-W.Va.) overwhelmed Senate opposition yesterday in his effort to weaken the strip mining control law, but House supporters of the three-year-old act predicted they will win in the end.

By 61 to 32, the Senate voted to limit debate on Byrd's effort to attach to an unrelated House-passed bill a provision freeing states from following federal guidelines in drafting reclamation plans for abandoned strip mines. That vote, one above the 60 needed, assured a Byrd victory when opponents ran out of time and he needed only a majority vote to pass his proposal.

Sen. Howard Metzenbaum (D-Ohio), leader of the opposition, called Byrd's heavy assault a "power play" on behalf of "special interests" that would "devastate" land where coal is mined from the surface.

The Senate had approved the same bill last year. But when it went to the House it was referred to the Interior Committee where Chairman Morris K. Udall (D-Ariz.) has sat on it since. This year Byrd seized on a minor bill that came out of the House Merchant Marine Committee, so when it returns to the House, Udall won't be able to get his hands on it.

But the House would have to vote on the issue eventually and Udall predicted yesterday that the vote would sustain the strong 1977 act and reject Byrd's attempt to water it down.

"We have talked to the speaker and he will cooperate with us," Udall said. There are several options facing the House when the strip mine bill reaches it. There could be an attempt to accept the Senate bill as is. That requires unanimous consent, which it couldn't get, or a resolution from the Rules Committee. Speaker Thomas P. (Tip) O'Neill Jr. can control the Rules Committee on most issues. The bill could be sent to a House-Senate conference, but if the Byrd provision stayed in, it would be subject to a separate vote when returned to the House. Or the bill could just die without further action.