The standing committee which plays a crucial role in the ability of the Speaker of the House to

exert influence is the

The correct response is the House Rules Committee.

Explanation:

The standing committee that plays a crucial role in the ability of the Speaker of the House to exert influence is called the House Rules Committee. This committee decides whether the bills that are reported from policy and fiscal committees will be presented for consideration, and in what order they will appear on the House floor. It is also the responsibility of the Rules Committee to review the floor resolutions and to decide whether to adopt them and then schedule them. The Rules Committee is also called "The Speaker's Committee" because the Speaker of the House can use it to control the Floor and what is discussed and passed. The Rules Committee was traditionally chaired by the Speaker themselves until 1910.