This law is so stupid that it turns out and becames really funny.
You might have american citizens who are the descendants of lincoln - but just because they forgot to pay some "money" - they are not americans anymore.
Punishment and vindication seems to be american way.
This doesn't have to do with citizenship, as far as I understand. I think it would hinder people's ability to travel, for people in the US. For Americans abroad, it'd have more serious consequences and would likely affect their daily life, but they'd still be Americans.