The Small Business Job Protection Act of 1996 tightened the rules for claiming dependents.
No ID, No Credit
The IRS now has the authority to deny the dependency exemption and the dependent care credit if you fail to provide a correct Taxpayer Identification Number (usually a Social Security Number) for each child or dependent claimed.
Mathematical Error Treatment
If you miss an SSN or provide an incorrect one, the IRS treats it as a "mathematical or clerical error." This allows them to summarily assess additional tax without going through the deficiency procedures that normally allow you to appeal to the Tax Court beforehand.
Impact
For a family in the 28% bracket, losing one exemption and the childcare credit could cost over $1,000 in additional tax. Ensure you have SSNs for all your children, including newborns (apply for one at the hospital).