After the Revolution, the US owed money to many including soldiers who served in the War. After a few years, it seemed like the payments would never be made, and speculators began buying up the debt at steep discounts. These speculators basically acted exactly like the "Vulture Funds" did in the Argentine situation.
Many were naturally for paying what was due to soldiers, and against paying off the speculators who were "preying" on the situation. By paying it all off, Alexander Hamilton demonstrated the (a) the US would make good on its debts and (b) US debts can be can be liquidated bought and sold freely without exception.
Both of these points make it easier for a country to obtain new finances on demand at lower cost. Point (a) means the lender can be assured the country will not disown the loan. Point (b) because debt which can be freely sold gives the lender much more flexibility.
[1] http://www.historycentral.com/NN/economic/Hamiltontorescue.h...