Politicians are primarily in the legislative branch. What constitutional authority do they have to determine the outcome or direction of such a process?
This executive order is aimed squarely at the executive branch, which the President controls.
Some wasteful spending is explicitly contained in laws passed by Congress and signed by the President. The President is sworn to faithfully execute those laws.
Fuurthermore, Trump is a negotiator. He is likely to negotiate on both this and other topics. The more pressure we put on the politicians he negotiates with, the better the outcome of the negotiations.