For the purposes of this question I am going to assume "cloned" means that somatic cell nuclear transfer was involved. As a U.S. citizen I am going to restrict myself to "President of A Nation" being the U.S. president because I am not as familiar with other presidential offices abroad.
Just the act alone of switching the U.S. president for a clone would be an incredible feat. For it to be successful at least some part of the executive branch would have to conspire to accomplish it meaning that part of the government would be aware of the facsimile. As conspiracies go the less people involved the better. As the old saying goes, "Three may keep a secret if two are dead.".
Clones also aren't the same age as the original. The clone has to be born and raised. Article 2, Section 1 of the U.S. Constitution sets the minimum age to be president at 35 years old. That means any conspiracy to clone the U.S. president would have to anticipate decades ahead of time who would grow up to become the U.S. president and have the cloning technology. The technology to successfully clone humans isn't known to the public to fully exist today, let alone decades ago by scientists. Except for time travel the only scenario in which it would be likely is if a huge breakthrough was made decades ago and the Invention Secrecy Act classified the patent to clone humans.
The other problem is the entire cloning process itself. Cloning doesn't transfer memories and knowledge from the original to the copy. This means things such as personality, skills and habits would most likely be different.
Even if the mind could be copied and transferred natural genetics is random. Just because something is a genetic clone doesn't guarantee the copy would look exactly the same because of factors such as environment and genes being expressed differently. The first cat cloned by scientists, named CC, had different colored fur than the original cat.
So you could try and clone the U.S. president to bring down America but the resulting clone may look different from the original. The clone might have something like orange skin and if there's one thing I know it's that Americans aren't stupid enough to fall for a clone with orange skin. That just wouldn't happen.