While being both the head of state and head of the government is very taxing and time consuming, I feel that they can continue to be held by the same person. The American President has historically had both duties and has been able to do both.
Just look at a couple images of recent U.S. presidents side-by-side: a picture of the man on his original campaign trail and a picture of him after serving one or more terms. See the whiter hair? The more plentiful wrinkles? The expression of unbelievable tension? The stress of the presidency wreaks a havoc on a person that's not only real, but that is also manifest right on the face of the Head of State. This is one of the reasons that I make it a point to only speak poorly of policies, not of presidents, because I admire the fortitude it takes to merely function day to day under the stress of being one of the most powerful, but also most pressured, people on earth.
That being said, I do agree with previous posters--the president has many people and much money beind him (hopefully "her" someday as well...) He's got everything he needs to do the job. But I think we do need to acknowledge that it is one beastly job to do.
I tend to agree with those who are of the opinion that this is not too great of a burden for one person. The way the US government has been organized (for its system of checks and balances) for so long almost makes it inevitable that no single person has a burden that is too large to bear. Not only this, but the president of the United States retains an entire cabinet of trusted advisors, as well as other personal advisors so that his job and opinions are always balanced by and supported by the opinions of others.
I would say no because of the way the US Congress is set up. Unlike countries where there is both a head of state and a top parliamentarian, the US president is not a member of Congress. This means he is a chief executive and not also responsible for creating legislation.
I am assuming you mean the American President, though the structure of the dual role is common in other countries without monarchies. The burden of the job is incredible, with very long hours, unbelievable physical and mental stresses, family pressures, and during that time you must also consider running for election while still performing all of your duties.
But this stress and pressure is nothing new. Washington, Lincoln, FDR, George W. Bush and Obama all experienced the similar pressures of economic frailty and wartime decision-making. But along with the stress that goes with consolidating such power into one position goes efficiency of decision-making as well. The American Presidency has an immense amount of power behind it, and can act decisively when necessary.
As head of state, it is an important office for creating an image of a stable, prosperous, strong nation, for both our own citizens, those of foreign countries, and for financial markets.
I would argue that it does not. The duties of the head of state are not very many and are rather easily accomplished. Heads of state only have to do a few ceremonial things. These tasks (like representing the country at foreign funerals or like showing concern for the victims of disasters) are not ones that take a great deal of time and/or effort on the part of the president. This means that a president who has both duties (like the US president) is not terribly overburdened.
As head of state, a president is a largely ceremonial figure; responsible for representing the country at international events, involved with rallying national sentiment and energy in times of crisis or need, critical in the role of helping to facilitate communications between the government and the citizens of the country.
As head of government, a president has a leadership responsibility along with some ceremonial duties; primary spokesperson for the policies in place or being advocated by the government, decision-maker in determining government actions and policies, involved with selection of individuals to fulfill other government duties, representative of the government within the country and abroad.
Your assignment is asking for your opinion in answering the question. Examine the evidence and decide how you feel. One variable not mentioned above is the "style" of the president - some leaders may be capable of delegating or managing time and effort so as to fulfill both roles simultaneously and constructively, while other leaders may not be capable of doing so.
I must agree with the above posts that both positions can be handled well by one person. While it surely is taxing, exhausting and time-consuming it has been done well by many Presidents. Economic downtimes, wartime and global issues will always be a part of politics and having one person who can address both domestic and foreign issues is an advantage. At a time when we have become a global society and when our economy is linked critically with other nations it could be said that one person best handles the interdependent roles.