http://www.inteconlaw.com/I-9_counseling.htm
The first list are the documents which can verify employment eligibility without any further evidence. Otherwise you have to show two original documents from the other two categories. Basically a valid ID, and proof that you can work here.
No where is a Tax ID number mentioned. It is not an ID, and it is not verification that you are allowed to work here.
In Las Vegas, they do an extensive background check that takes about 3 months for many jobs. I am sure that people may offer the tax ID number to conduct the background check, since these people do not have a SSN, but this does not satisfy the requirements for the I-9 form.
DOCUMENTS WHICH ESTABLISH BOTH IDENTITY
AND ELIGIBILITY FOR EMPLOYMENT
1. United States Passport
2. Certificate of United States Citizenship (Form N-560 or N-561)
3. Certificate of Naturalization (Form N-550 or N-570)
4. Unexpired foreign passport which: Contains an unexpired stamp which reads "Processed for I-551. Temporary Evidence of Lawful Admission for permanent residence. Valid until _[date]_ employment authorized"; or has attached thereto a Form I-94 (little white card) bearing the same name as the passport and contains an employment authorization stamp, so long as the period of endorsement has not yet expired and the proposed employment
is not in conflict with any restrictions or limitations identified on the Form I-94.
5. Alien Registration Receipt Card (Form I-151) or Resident Alien Card (Form I-551) (commonly called a "Green Card"), provided that it contains a photograph of the bearer.
6. Temporary Resident Card (Form I-688).
7. Employment Authorization Document (Form I-688-A).
DOCUMENTS WHICH ESTABLISH IDENTITY ONLY
1. State-issued driver's license or state-issued identification card containing a photograph.
2. School identification card with a photograph.
3. Voter's registration card.
4. United States military card of draft record.
5. Identification card issued by federal, state or local government agencies.
6. Military dependent's identification card.
7. Native American tribal documents.
8. United States Coast Guard Merchant Mariner's Card
9. Driver's license issued by a Canadian government authority.
DOCUMENTS WHICH ESTABLISH EMPLOYMENT AUTHORIZATION ONLY
1. Social Security card, other than one which has printed on its face "not valid for employment purposes." Note: This must be a card issued by the Social Security Administration; a facsimile such as a metal or plastic reproduction is not acceptable.
2. An original or certified copy of a birth certificate issued by a state, county, or municipal authority bearing an official seal.
3. Unexpired CIS employment authorization.
4. Unexpired re-entry permit (INS Form I-327).
5. Unexpired Refugee Travel Document (INS Form I-571).
6. Certification of Birth Abroad issued by the U.S. Department of State (Form DS-1350).
7. United States Citizen Identification Card (Form I-197).
8. Native American tribal document.
9. Identification Card for use of Resident Citizen of the United States (Form I-179).