IMO the USA is incapable of backing the Greenback with gold simply because of the amount of greenbacks in circulation globally. It has printed dollars incessantly since the end of the Viernam War/end of its gold standard. The reason it pulled the pin on its dollar gold backing is that Fort Knox would have been cleared out within a decade had it not done so. Given the Trillions of USDs floating around the world at present and the challenges faced by the USA economically, if the US decided to back the Greenback with Gold, customers would opt for the Gold (as did DeGaul did in the early 70s) to balance trade.
In summary, the US problem is the structure of its political economy which is relying on $2 trillion annual budget debt (deficit) to stay afloat.
PS: If the US could afford to back the USD with Gold, then there would be no need to run a $2 Trillion annual budget deficit.