There were many problems faced by the new American government. I will mention two that were very important.
The first of these was a domestic problem. This was getting the states to be happy in the new system where they had so much less power than they had had under the Articles of Confederation. A crisis in this regard came in the Whiskey Rebellion. This was an incident in which some people in a state rebelled because they did not like being taxed by the national government. Washington had to overcome these sorts of opinions to create a true nation.
The second was a foreign policy problem. After the French Revolution, France and Great Britain came into conflict with one another. The US had to decide what stance to take with regard to this conflict. The conflict led to dissension within the US and to dangerous decisions that had to be made so as not to antagonize either France or Britain, both of which were much stronger than the infant US.