Oh, I so hoped I'd read some great answers here.
Can you do any part of your job working from home? I am a full time telecommuter, but I can't get anything done when either of my kids are home sick. The best I have come up with is to find as many local jr high and high school girls who can at least stop by when their school day is over and let me work for 2 hrs or so at the end of the day. (The other advantage with this type of mother's helper is for snow days. The excessive snow days just about killed my productivity at work last year before we realized we needed to start stalking neighborhood teenage girls to get them on our babysitter list.)
I have tried sittercity.com to find last minute babysitters, but the trouble is no one ever responded to my requests at the last minute. So maybe you can use that to find a sitter ahead of time who can be "on call" for sick days. It never worked for me.
Also, I was in a MOMs club, but my kids never really form attachments to the other kids since most of the activities were during the week when I was working. I noticed amongst the other moms who were more core to the group a lot of support for helping take care of other people's kids, but not so much when the child was sick... . Moms tend to be scared of other kid's germs. Justifiably.