And they would continue to do so.
The US dollar is supported by the productivity of the taxpayers and the full faith, credit, and taxing power of the US government.
And it would continue to be.
So, what do the eastern states in particular produce that contributes to the value of the dollar?
I'd suggest you check the breakdown of GDP by state. Nine of the ten largest state economies voted for Obama last year, Texas was the only exception. The wealth is there, and the goods need to be purchased.
It is a scary thought to contemplate a world without a US dollar. But, consider for a moment, the direction the present administration is taking. When asked how much money he planned to borrow, Obama stated on national television "as much as we can". If that doesn't make your hair stand up, nothing will. That's why the talk of secession is starting. The productive states do not want to be stuck with the bill.
The "state" with the highest GDP by far was listed as the District of Columbia. I don't think there is much mining, farming, or manufacturing going on there, so I assume this high rank was achieved in the "service" category, specifically government services. Most conservatives would say, non-productive government services. In any case, services which do not produce wealth, in fact they waste it.
Next in line are Massachusetts, Connecticut, New York, and Delaware. There is some manufacturing in these states. However, I think there are lots of "knowledge based" industries and financial services companies. If the excrement really hits the ventilation device, these industries will collapse, fast.
Next is New Jersey. Some manufacturing but a lot of knowledge and service based industries.
At seven and eight are Colorado and Alaska. These states actually produce real wealth that people need, energy, basic materials and food. By the way, Texas is 20th.
My point is that knowledge based industries, financial industries and government are only sustainable when they are based on strong agricultural and manufacturing sectors. Cheap, plentiful energy underlies the whole shebang. Take away cheap food, cheap plentiful energy and a manufacturing base and the service industries cannot survive.
Don't be so sure about the survival of the US dollar. Your current administration seems to be hell bent on destroying it. Someday, soon, they may succeed.