(Thanks to Travis Holte)
UPDATE from Vadim Antonov:
The real threat of national ID cards is that they constitute the government's permission for gainful employment.
If the government issues them, the government also has power to take them away — just like they have the power to take away or deny renewal of driver licenses.
Eventually this power will get used for coercive purposes — you didn't pay parking tickets, you won't be able to get a new driver license, etc. This path leads to the use of this coercive power for social engineering purposes.
The final form of this permission-to-work "National ID" scheme is what the Soviet Union did to the peasants to keep them from moving to the cities — simply not issuing them the papers necessary for obtaining "propiska" (registration) in a city. Later, it also became the major tool for stifling political dissent — quite a few dissidents (and other threats to the regime such as amateur rock musicians) found that they can't get a decent job and are reduced to subsistence living and occasional menial jobs — or that they are exiled from big cities.
What this National ID card amounts to is giving the government the power to impose a stiff penalty — condemning people to poverty or exile — without inconveniences such as courts and jury trials being involved.
UPDATE from Bill Young:
Though we would not bear it on our foreheads nor right hands, functionally it is the mark of the beast.