1) Say No. If you need to, practice several times out loud and in your mind. "I've given it a lot of consideration, and I don't feel that I would be able to provide the level of care your baby will need in addition to my own family."
((This will probably not be the only time you're asked to do this kind of thing as a stay at home parent... just follow the link at the bottom))
2) If she argues or tries to convince you at ALL... thank your lucky stars you didn't say yes!!! Anyone who can't see that someone else has a full and busy life, that being a childcare provider is a full time job, and is just blind to other considerations is NOT someone you want to be having to deal with in a nanny situation. They will use and use and use you (and ignore, and ignore, and ignore... like bringing over a sick baby/child even when you've said not to, not "let" you take vacations "Oh can't you wait until ________,". You'll here the words "just" and "can't you" and "oh it won't" and AWFUL lot with these types of people.
3) DO let her know as soon as possible (so she can work on another alternative)
4) BE VERY WARY about accepting provisionally "Until you can find someone". I did this once, to cover a "2 week gap" between nannies... that turned into MONTHS. I can't even count how many other people I know who have been suckered into the same position.
And for moral support... I was climbing the walls a few years ago becuase EVERYONE (it seemed) seemed to equate that I was a SAHM with =ing I had no life and "should" be their babysitter. Paid or free, it doesn't matter. Many of whom would argue with me (wth?), just show up anyway, etc. There was an outpouring of support from other SAHPs and WPs who would never make such presumptions. I'm NOT saying your neighbor is like this (but once bitten, twice shy)... but that outpouring has a lot of chutzpah behind it! :) :) :)