I don't know. Social Security Numbers (SSN) we have are a national ID number in pretty much everything but name. And even though they are explicitly not supposed to be used as identification (it says so on the card), that's how it's used 99% in practice.
It's definitely possible, but much more unlikely than going without a passport, for two reasons:
1) The expanse and culture of the U.S. favors driving cars, so most people learn to drive a car. A driver's license is most people's form of photo ID.
2) A puritanical history makes for strict age limits on alcohol and tobacco; young adults must show photo ID in order to enter many bars and clubs where alcohol is served.
These two factors mean that most Americans have an ID by the time they are 21. In fact, I don't know anyone who doesn't have one.
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