Would be easy to implement, but hard to manage (what if govt loses privkey for printing money?) and build trust (what if next congress decides to stop this currency).
#1 could be solved by having a scheduled key rollover system, anchored robustly by the central bank (eg public display of key fingerprint at headquarters).
#2 doesn't sound any different from other fiat currencies or bonds issued by nation states. It's in the issuer's ecnoomic self-interest to preserve their credibility.