US currency isn't backed by gold- it is in a sense backed by the US government. BTC is wholly unbacked.
And to some extent it is currently based on the ability of the United States to protect its interests overseas, the trading of oil in the US dollar and significant trade partners accepting the US dollar as a means of exchange for goods shipped to the US.
And that works as long as significant portion of the world continues to believe in all of the above, if that should ever stop I hope I won't be there to watch the carnage. That's the kind of 'interesting times' that one would hope to avoid.
There for, the US gov't (or more correctly, the Fed reserve) can print their way out of debt that they owe to third parties, until those third parties all wise up. But then you got 11 air craft carriers paroling the world, untold number of submarines and missiles, massive air force etc, and if the US gets a whiff that you are no longer denominating your goods (e.g., oil) in USD, you might find yourself being called the axis of evil.