I'm looking for a payroll service that I can use with a nanny. 
However I'd like to fund the payroll service with a credit card
(rather than have the service pull money directly from my bank
account).  Does such a service exist?

Hi Badgers-Ga,

As it happens, there is a company set up just for that very purpose:
http://nannytax.com/

You can pay them by credit card. 
But it's not clear if you can pay the taxes by credit card, too. 
You'll have to ask them.

Generally, when you do pay taxes by credit card, you are charged
an extra 'convenience fee' to cover the cost that the merchant
would normally pay, since the tax authorities don't pay merchant fees.

The NannyTax folks aren't cheap.

So you might want to shop around and see if the prices
offered by the regular payroll services are any lower.

Here are the major services:

Paychex -  http://www.paychex.com/

Intuit - http://www.payroll.com/

ADP - http://adp.com/

Just call their toll-free numbers and tell them what you need.
Any of their staff should be able to help you. 

Incidentally, have you thought of asking your tax professional to do it?
They'll often do it for less than the payroll services. 

AND they'll integrate the Schedule H into your tax return, and make
sure all the state taxes are taken care of, too. 

Best wishes, 

Your TaxMama -ga

I wanted a firm who accepts credit cards; this answer didn't give me
that information directly.

I'd say she gave you a pretty good answer for $5...  call them yourself!

Badger94...    dude, you owe TaxMama for this post. 

She answered it just fine.  You can pay NannyTax with a credit card
for their services, and since they specify that they don't pay the tax
bill for you (they only do the paper work and YOU pay the bill), then
you can just pay the IRS with your credit card. Duh!

You can pay both the professional services fee and the taxes witha 
credit card using this method. That's exactly what TaxMama told you,
so pay up!!!! [Google, please enforce this on the lame dude!]

I paid!