There are two issues here.
Claiming a credit on personal income tax for child care and paying the payroll taxes for the nanny as a household employee. The payroll taxes impact the employee. The tax credit does not.
It would be hazardous to try to take the credit without paying the nanny taxes. An IRS audit would pick it up.
Here is the IRS publication on payroll taxes for household employees, including nannys:
Publication 926 (2011), Household Employer's Tax Guide
As a nanny, if you are paid more than $1700 in a year, your employer
must pay social security, Medicare, and federal unemployment taxes. Giving you a form 1099 is not an option. It would be illegal. In the long run, you receive credit toward your social security account for every quarter you and your employer pay into it, credit toward Medicare benefits later, and the option of filing for unemployment if you lose your job.
Workman's compensation laws vary from state to state. By paying workman's compensation taxes, you and your employer are covered if you are hurt on the job.
Unemployment tax and workman's comp are totally paid by the employer.
State income tax, where it exists, also has to be withheld, and state unemployment tax.
If you accept payment under the table, you will likely be paid less. What you save on taxes now you will lose in future social security benefits.
It has been a long time since we had a nanny. We paid all her taxes, including her share of the social security tax (which was lower than it is now.) And, yes, we did claim the child care credit when it became available.
So, I would be leery of an employer who does not want to do the payroll taxes. It's a pain in the neck to do the paperwork for one employee, but it has to be done. There's probably an app for it now!
What you will be responsible for is your federal and state income tax (if your income is high enough to owe any), your share of the Medicare tax (1.45% of your salary), and your share of the social security tax (4.2% of salary this year). The employer has to match the Medicare tax and pays 6.2% to social security. Usually, employer and employee pay the same to social security. The employee rate was lowered this year.
See here about pay:
Tips: How Much Do I Pay a Babysitter
Be sure you know what you will be expected to do in addition to baby care, laundry for example. If you do additional duties such as cooking or cleaning house, you should get paid more.
If you will be driving an employer's vehicle, make sure his insurance will cover you.