There's a limited number of Bitcoin in existence, and with each one you buy (issuing an IOU in return), the price goes up and people doubt your ability to pay back more and more.
This is almost exactly what's happening with Puerto Rico's debt crisis [1]. They've sold a bunch of bonds, were downgraded to "junk status" in 2014, and then defaulted on a bunch of them in 2015. Eventually you have to face the music and cannot borrow any more.
[1] https://en.wikipedia.org/wiki/Puerto_Rican_government-debt_c...
Sure, they're traded at very close to face value, but that's because traders trust the US government to pay. That's different for governments considered at risk of default. That could also become different for the US government, if the economy really goes south or if enough people start talking about defaults.
I don't see how criptocurrencies would change any of that. For how much less than 1 BTC would people trade a 1 BTC IOU backed by the US government?
Edit: As it stands now, there is a "lender of last resort" that can create new money as needed to fill in the gaps if those two account holders want to get their money out, so there's no need to distinguish the original vs bank-created money. But you can't create new Bitcoins, so there is a reason to distinguish Bitcoins on the blockchain vs those IOUs.
>that money might simply be borrowed
...but I don't think any cryptocurrency would have any effect on any government's hability to borrow money. What would stop a lender from trading 1 BTC from a note saying "I.O.U. 1 BTC"?