[albertyw]

Sorry to be pedantic, but the US dollar is not backed by US government taxation. A dollar is still quite valuable outside the US because people and institutions attach a value to the US dollar, mostly because the US economy has been the largest and most open economy in the world for several decades. Taxes set by the Treasury, like all other market forces, change and are changed by the rest of the economy.

Your example is a classic example of exchange rate problems surrounding floating currencies. Since both the USD and bitcoins are free-floating (though there are powerful institutions stabilizing the USD such as the Fed and IMF), there would be an onus to convert USD into Bitcoin until the relative value of USD was high enough to offset the conversion deficit. That, or there would need to be equally powerful institutions behind Bitcoin to buy other currencies, but it would be very hard given that there is a practical limit to the total number of Bitcoins in and out of circulation.