Control implies complete authority for the day-to-day workings of a thing, and there's no way a President could do either of those things. If he did, we'd probably have to refer to him as Tsar or Emperor or King. No one person should have so much control, even if he could find a way to make it work on a daily basis.
The issue of "control" might be where some ambiguity results. There are elements of daily life in these programs that cannot be "controlled" by the President. This is why others are placed in those positions so that they can manage the day to day affairs of such programs and report out on their status to the President or to someone close to him/ her. The President can immediately control these programs and change their course when he/ she sees that they might necessitate an alteration. For example, when Former President Bush understood that then FEMA Director Michael Brown came under severe criticism for his lack of efficiency in handling the crisis in New Orleans, he was asked to resign. Another example of the President being able to exert control over the programs of the federal government would be in the wake of the September 11 attacks when the creation of Homeland Security was meant to streamline the process of how the federal government provides domestic protection. In both examples, the President was able to exert direct control over programs and alter or modify its direction/ responsibilities when it was perceived that a change was needed.
Absolutely not. That would be an impossible job. You just have to remember that over the last century the size of the American government and its agencies and sub-agencies has grown along with our economy and population, so that the President has tens of thousands of employees to help maintain the government bureaucracy and its various tasks, and dozens of cabinet members, advisers and staffmembers to help him direct them all.
Luckily for the President, the vast majority of these programs are not new, have been running for a long time, and we have well trained personnel who make entire careers out of steering the ship, so to speak. All the President has to do is give them some direction when they need it, and make sure they are funded in the budget each year.
There is no way that the president can control a government of the size of the United States government. Presidents have limited amounts of time and energy and cannot have any hope of personally supervising the whole government.
This is one reason why presidents cannot really accomplish as much as they set out to. The various government agencies have ingrained customs and habits that they are not likely to change unless forced to. Therefore, to cause changes to happen, presidents must actually take note of what is going on in an agency and spend the time and energy needed to change that.
Since presidents can only do this with a very few agencies, the vast majority of the government goes along doing what it wants to regardless of what the president might want.
In a vast, and highly developed country like the USA the multitude of so many programs and activities undertaken by government is something that is unavoidable. Whoever is the head of government has no choice but to accept the overall responsibility for managing these. For example, in USA the President is the head of government while in India the Prime Minister occupies that position. In both cases the head of government has manage the entire set of governing activities and programs. In a situation like this, it is not a question whether the President can control a government with so many programs and responsibilities. The question is how well he can do this, and what ways can be adopted for doing so.
The answer to these revised question is that president is able to manage the affairs of government, not by trying to manage the each and every activity of the government directly, but through an effective organizational set up. The president gets involved in direct management of only very important activities. For other activities the work is handled by the government organization, and the president only manages the top officials in the organization. Another method adopted is to obtain and review information on the overall situation of the country. This enables the President to identify, from time to time, areas where his greater involvement is required.
Please note that the fact that most of the work of government is done by the organization without direct involvement of President does not mean that the government officials do what they want regardless of what the President might want. Effective management of organization ensures that the government machinery by and large works toward the direction set by the President.