We tried that from 1776 to 1787. It was called "The Articles of Confederation." It was a spectacular failure. Congress had no way to force the states to pay (just like the NRST) and so some didn't.
To compare the situation under the Articles of Confederation to what would occur under the NRST is absurd.
The Federal Government of today has more than enough power to collect the sales tax from the several states.
The Articles of Confederation didn't work at the time because of the frameset of the population at the time.
For starters, we didn't have much of a standing army.
Today, I don't think there really is a militia, in the Revolutionary sense, and the fact is, alot of places rely on the military for their economy.
Any state that refused to contribute, you close all public installations, it's that simple, because states will do anything to keep their respective military bases.
You could also make it requirement that, in order for someone to become President, their state has to be in compliance, set the same level for Congress. Because there will still be something for the feds to do, and no state will want to lose their influence.
In the end though, any solution for government finance is going to be a dressed up form of extortion.