While the House lumbered through a third day of debate on its big $4.4 billion water resources bill yesterday, the Senate was neatly passing a smaller bill of its own.

With only five members present, the Senate by voice vote authorized a $200 million flood control project avidly sought by Majority Leader Robert C. Byrd (D-W.Va.) for his home state.

The project, opposed by the Carter administration and the Army Corps of Engineers, was attached as an amendemtn to a noncontroversial bill that attracted little attention.

Byrd's project directs the corps to provide flood control along the Tug Fork, a stream that divides West Virginia from Kentucky, even though the required cost-benefit studies have not been conducted.

That same project would be authorized at a $100 million level in the larger bill being debated in the House. Again yesterday, Rep. Robert W. Edgar (D-Pa) was defeated on a number of attempt to reduce the size of the bill and force serious debate on national water policy.

A final vote on the bill, which faces almost certain veto by President Carter, had been scheduled for last night. Action was suspended when a number of members demanded more time to argue their amendments to deauthorize 20 controversial projects.