there is something called "child credit". per IRC sec. 24. it is different from the dependent care program ($5k deduction) provided by your employer. IRC sec. 129. normally, if you are enrolled in the dependent care program, then you are not eligible to child care credit. (no double dipping rule). if your employer provides dependent care program, you can still elect not to participate that program and get the child credit. it works out better for some people.
child care credit is just one-line on 1040. no need to have SSN from your nanny.