Nanny Taxes (I know a much hated subject)

Ok, so I am new to this whole nanny thing. I just recently received a full-time nanny job offer from a family who too is new to this line of work. When I asked the employer about how taxes would be handled they answered me, "Well, if you want to pay into taxes you can do it on your own. It is easier that way." I guess I am just sort of confused after having read several online posts of the requirements for employers as to what I should do. These are my questions. Any insight would be gratefully received.
Should I...
1. Take the job and just forget about it, which I know is wrong?
2. Take the job only if the employer is willing to pay the applicable taxes?
3. Just turn down the job and hope something else comes along? (Just a heads up, this is my first full-time job offer of any type since graduating from college last May. The job market stinks right now as most of you know and so this would be a hard option to choose and the job does offer a rather large paycheck.)
Thanks for any help.

I hope I did not catch this comment too late, or you have convinced your employer to do the right thing and pay taxes. Even if you were to pay into taxes on your own, your employer is still obligated to pay their portion of the taxes. I actually work for a payroll company that specializes in household employees. Many employers do not want to pay taxes because they see it as a hassle, but then are not thrilled when they get caught and fined for breaking the law. Paying illegally can hurt you in the long and short term. From not being able to prove income to get loans, to being older and having no money in your social security because you were paid off the books. If you would like more information for yourself or to pass on to your employer visit www.GTM.com. We make the process painless for employers and employees alike and you do not have to worry about breaking the law.