what should i say to a family, as a potential babysitter for them?

I've been talking to a family (via a childcare provider website), about me being there full time babysitter for the upcoming summer. I emailed the parents on the 23rd, and on the 26th they responded saying they might be interested in hiring me. That same day (26th), I replied telling them a bit more about myself, etc. Granted, it's only been about a week, plus both parents work full time, plus they have a child- but I was wondering...

1) if/when it would be appropriate for me to email them again-- & maybe see where they currently stand on everything? I'm not trying to be pushy- but I need a definitive answer.

2) if/when i contact them-- what should i say, that wouldn't sound rude? basically, i feel like they need to know that i will soon have to start looking elsewhere if i don't hear an answer from them. but obviously i don't want to say that to them... suggestions?

3)...or should i just not contact them again- & continue to talk with other families that i could potentially babysit for? i guess part of me feels like that would be wrong, b/c that family did seem interested

Keep looking, you might get a better offer. If someone wants you they will let you know.