No, I don't think Congress passes laws to determine fees. The agency would do that.
However, I heard that Congress is mulling the idea of cutting funds for social security cards. Thing is...how do you get Obama to sign it?
They can't. But they can make it very difficult for the 10-12 Senators from blue states that would need to vote to override a veto. Even in deep blue states like Oregon, this immigration BS is very unpopular.