The leaders of the American Revolution were not at first considering changing the government. They and many people were upset because they felt that the British Parliament was denying them their rights as Englishmen with such issues as taxation without represtentation and import and export bans. However, when it was realized that reform was not to be gained without a long drawn out war, it became clear to the leaders of the time that they would have to declare a new nation, although at the time they had no idea of the form of that nation. According to many historians, one of the main reasons they declared themselves a nation was simply to be able to apply for help from England's enemies such as France.
It was not until after the War when Washington refused an offer of a crown, that the leaders of the revolution were able to take the time to truly consider what type of government that they would want to create. Their creation reflects the Enlightenment philosophy of the times.
It was less about changing the type of government, and more about creating a nation with a new type of government.
The more cynical view is to say that Americans seperated themselves from the British because they--the colonials--wanted to be imperials.
Americans had been experimenting with government since the founding of the colonies.
Only when the colonies became important to the British Empire did Parliament and the King attempt to make the colonies pay their share of costs as a member of the empire.
American elites, the ones who controlled the upper and lower houses of the colonial legislatures, struggled to define what exactly the new type of government would look like. Many did imagine it would be a republic. Educated gentlemen would court the votes of landless men. But there would be no direct democracy.
The war did not change that view. That image basically stayed the same throughout the war. The only people who objected to this republican vision were the landless, and the new class of businessmen who ran for office in the lower assemblies. During the war, this rising class of men struggled to participate in colonial politics. When the decision was made by the Second Continental Congress to declare independence, a wave of constitution-writing fever hit the colonies, and each newly sovereign state wrote constitutions that attempted to settle the issue of representation: who could participate; who could vote.
With that, the argument over who would rule the newly created United States took shape during the war. Yet it did not affect the constitution of the U.S. during the war--the Articles of Confederation. Yet it can be argued that, with the creation of new state constitutions, the seeds of the change of governmet were expressed during the war.