That depends upon how one defines “government”. In non-US usage, the President would fulfill all functions of a “head of government”. Cabinet Secretaries report to him. He is the Commander in Chief of the armed forces. The daily business of administering the government falls under his office or under the cabinet offices and departments that are under him.
In the US use of “government”, the USA has no “head of government” at all. In the USA, when we refer to the “government”, we usually refer to both the Congress and the Presidency. If speaking. Sometimes we remember that the Federal courts are the “third branch” of our government, but we tend to ignore them since they are appointed.
So, under the US usage, the President, the Speaker of the House, the Vice President (as President of the Senate), and the Supreme Court of the United States (as a body) are the “head” of our government.
I must take issue with this blatant lie regarding the USA. Believe it or not, the press’s portrayal of conditions here is not necessarily the truth. Nobody ever even remotely was induced by seeing anti-Bush protests to believe that there would be any attempt at a coup in the USA.
So, then Queen Elizabeth II is free to set whatever treaties may strike her fancy when she operates as “head of state”. Likewise, she is free to set relationships among members of the Commonwealth as suit her fancy, since she is “head of state” of all those countries.
Of course not. Don’t be silly. A constitutional monarch never exercises her or his powers in the monarch’s own personal, unfettered discretion. But the nation’s role in the international community is exercised in the monarch’s name, regardless of what role the monarch played (or not) in the internal constitution that resulted in deciding that role. For example, look at the treaty establishing the European Union:
You would think, from the treaty, that the European Union was just something that a dozen individuals agreed to. But those dozen individuals are not acting in their personal capacities, they are acting as heads of state, subject to whatever institutional and political constraints their constitutions and cultures impose.