Under the tax law - babysitters are required to report their income on tax returns regardless if you reported that income to the IRS or not.
In additional - such income is generally classified as self-employment income and both self-employment and income taxes may be due.
My babysitter refused to provide me with her social security number. Can I still claim the amount I paid to the babysitter for child care while I worked? If so, how do I claim these child care expenses on my tax return?
Yes, if you meet the other requirements to claim the child and dependent care credit, but are missing the social security number or other taxpayer identification required ID number of a provider, you can still claim the credit by demonstrating "due diligence" in attempting to secure this information.
If a provider of child care refuses to give the identifying information, the taxpayer can still claim the credit however, the taxpayer must provide whatever information is available about the provider (such as name and address) on the form used to claim the credit Form 2441, Child and Dependent Care Expenses, or Form 1040A, Schedule 2, Child and Dependent Care Expenses for Form 1040A Filers). The taxpayer should write "see page 2" in the columns requesting the missing information. The taxpayer should write at the bottom of page 2 that the provider refused to give the requested information. This statement will show that the taxpayer used due diligence in trying to secure and furnish the identifying information.
source - http://www.irs.gov/faqs/faq7-1.html
I hope that helps. Without SSN - you likely will not be able to file electronically - but should submit a paper return. I can't say for sure if that will trigger audit - but it is possible and you will be ask for record or other prof of your payments.