Gross. Always negotiate on gross salary. Otherwise, why wouldn't a nanny claim "0" deductions, get the largest possible amount taken from her check, and then get a huge refund in April, all the while you are "making up the difference" so that she nets $17-$20/hr.
Or, don't pay legally. I'm not willing to do that, so I negotiate on gross, pay my portion of FICA, pay unemployment insurance, and pay for Worker's Comp. I withhold the employee FICA, Federal, and State income taxes.
If your range is too low for where you live, you'll know because you won't find candidates.