Following is the law on documentation requirement for employment - ID's fall in two categories employment authorization and identity -It is required to have either one from paragraph B or one from C AND one from D. In other words, it appears that a SS Card AND a Driver's License is required if the employee does not have a Passport or Alien Card - so an illegal with a Driver's Privilege Card could NOT be hired, even with a fake unverified SS Card. (of course this is only my interpretation of this law)
Note that the Attorney General (US??) can prohibit the use of various forms of ID:
(B) Documents establishing both employment authorization and identity. A document described in this subparagraph is an individual's
(i) United States passport;
(ii) resident alien card, alien registration card, or other document designated by the Attorney General, if the document
(I) contains a photograph of the individual and such other personal identifying information relating to the individual as the Attorney General finds, by regulation, sufficient for purposes of this subsection,
(II) is evidence of authorization of employment in the United States, and
(III) contains security features to make it resistant to tampering, counterfeiting, and fraudulent use.
(C) Documents evidencing employment authorization. A document described in this subparagraph is an individual's
(i) social security account number card (other than such a card which specifies on the face that the issuance of the card does not authorize employment in the United States); or
(ii) other documentation evidencing authorization of employment in the United States which the Attorney General finds, by regulation, to be acceptable for purposes of this section.
(D) Documents establishing identity of individual.A document described in this subparagraph is an individual's
(i) driver's license or similar document issued for the purpose of identification by a State, if it contains a photograph of the individual or such other personal identifying information relating to the individual as the Attorney General finds, by regulation, sufficient for purposes of this section; or
(ii) in the case of individuals under 16 years of age or in a State which does not provide for issuance of an identification document (other than a driver's license) referred to in clause (i), documentation of personal identity of such other type as the Attorney General finds, by regulation, provides a reliable means of identification.
(E) Authority to prohibit use of certain documents. If the Attorney General finds, by regulation, that any document described in subparagraph (B), (C), or (D) as establishing employment authorization or identity does not reliably establish such authorization or identity or is being used fraudulently to an unacceptable degree, the Attorney General may prohibit or place conditions on its use for purposes of this subsection.
(2) Individual attestation of employment authorization. The individual must attest, under penalty of perjury on the form designated or established for purposes of paragraph (1), that the individual is a citizen or national of the United States, an alien lawfully admitted for permanent residence, or an alien who is authorized under this Act or by the Attorney General to be hired, recruited, or referred for such employment.