The US federal government could not put down Shay's Rebellion because of the weaknesses in the Articles of Confederation. The Articles of Confederation was the first constitution in the United States. This constitution gave the state governments almost all the power. The federal government, however, was very weak.
A perfect example of this was that the states were not forced to give the federal government military help/soldiers. When Shay's Rebellion broke out, the federal government had no way of organizing a military to stop it.