washingtonpost.com: 19 Terrorists Obtained Social Security Cards
"All 19 terrorist hijackers in the Sept. 11 attacks had Social Security numbers, and 13 obtained them legally, government officials say."
When you set up a system that's designed to cover everyone, you should not be surprised that everyone is covered.
SS numbers have been issued to visa holders for quite a while. Students and workers are issued them upon arrival. Only tourists make it in without them. If they impose a National ID card on us, then the terrorists will have one too. That's the whole point.