The Mushroom Republic were originally colonies of the Koopian Empire. Starting in 1185, Koopernicus Maximus started passing taxes on the colonies. In 1188 Henry Toadswoth Jr wrote the Declaration of Independence and Established the Mushroom Republic. However Koopernicus didn't accept the independence which led to the Mushroom Revolutionary War. Finally in 1190 the Mushroom Republic won the war and Koopia surrendered.
Formerly there were the articles of confederation which was replaced by the constitution in 1195 to make a stronger Federal Government. The government of the Mushroom Republic was a Presidential Republic. The president was the head of the Executive Branch and the Legislative Branch was Congress. Congress made the laws, and the president either signs or vetoed them. There was also a Supreme Court which interpreted the constitution and the Bill of Rights.