The best way that the presidency can change (increase or decrease) the scope of government is through the president's "bully pulpit." The president is the person who is most able to set the agenda for political debate. If the president wants to change the size of government, he (no women yet) can advocate for such a course of action by giving speechs, pressing Congress to act, and so forth.
The president cannot simply change the scope of government on his own. He can order a department to deemphasize certain things (have them stop investigating certain types of violations, for example) but Congress can always pass a law forcing him to rescind that order. A president cannot create or destroy a department of government without permission. Republican presidents have often talked, for example, about getting rid of the Department of Education. But since they can't do that by executive order, the department still exists.
So the president's best bet is to lobby the people -- to try to convince them that the government needs to be expanded or contracted.