1. Remember the show airs in Chicago in the morning, then more than once across time zones, so this will be an all day treat. We had a lot of buzz (Oprah's own forums went down under load for our show), and our URL was displayed on the screen. Regardless, you can expect a lot of traffic, mostly during the show and a few days afterward.
2. Your db will likely be your bottleneck. Make sure you don't have any unoptimized queries, or better yet, cache as much as you can so you're only hitting the db on writes for all the orders you'll be getting.
3. If possible, offload static content to a cdn. Akamai saved us here, because the site was not optimized size-wise.
4. What ultimately caused us issues was slow clients. I would definitely try to have a caching proxy up front. The snowball effect would cause us to tap out our 100Mb connection at times. Since you're using cloud hosting hopefully that's not a hard limitation for you.
5. It's really fun watching your bandwidth. I used a console tool called bmon. You'll be able to tell when commercials happen during the show.
6. +1 for a backup plan. Have a static page ready that you can switch over to. I'd highly suggest having an alternate payment processor, even if you have to go with Paypal. Since you're SAAS, you can't rely on retail or Amazon, so you may not get visitors to come back if your site fails. Make sure you can capture those customers the first time.
7. If you don't plan on having a free account, offer something so you can build your customer list and capture contact info. A whitepaper, newsletter, etc.
Have fun!