Proof of eligibility to work is one's Social Security card, normally. You don't need a birth certificate for that. Now, if you want to make the Social Security card a valid ID for the purposes of voting...

Somehow, the outrage about voter identity fraud - which empirically is so low that reported cases are in double digits across the entire country - is when it's election time, and politicians of a certain bent suddenly find out that poor and non-white people, for some mysterious reason, don't really support to cut top income bracket taxes even further.