Yup. The only way that I can think of would be to start with your DNA, and have a token generate time-based session keys that you'd use to authenticate against a central database. Of course, that requires the government having a sample of every single person's DNA in a database. (Big can 'o worms there) What would happen in the case of identical twins?
A perfect solution to this probably doesn't actually exist. I think you're ultimately going to have to go to something token-based. But you'd have to be able to guard against it being effectively a bearer instrument. i.e., if this person has this key, he is that person. You need at least two factor authentication.
Given data the government already has by virtue of the 'real-id' act, you could actually implement something like this. Take a digital hash of your fingerprint and use that as a part of the token. The other would be a passphrase or something similar. You could also tie it to a specific phone number that a temporary pin could be sent to.
The problem would be resetting any of this. Let's say that you burned your fingers so that your fingerprint has changed. How do you prove you are you? Or you lose your token. Now you have to go get a new one, and you need to authenticate to get it. Hopefully the fingerprint would do it, but if both were damaged at the same time somehow, authenticating will become much harder for you.
Needless to say the whole issue is really a big can of worms.
I agree. And I think James Madison would as well if were around to apply the observations he made on government to technical systems run by the government:
But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself. A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions.
--from Federalist 51