Once you have the characteristics by state/county/etc. (how the product is described legally), you can then cross reference it to where it is sold to and calculate a tax.
Is it a lot of data? Absolutely, but it is doable and the person/team who does it is sure to have a fairly large business charging companies who want their products sold online and companies using their system.
[ADDED] There will likely be multiple providers which should drive the price down and economic profits to zero. There is no reason why you would pick 1 tax calculator over another except price.
Most foods won't be an issue since they aren't sold as much online.
If you are a retailer of a new item with low volume, that is really where this is a problem. Once you make over a million a year in sales, you will likely have to hire an expensive consultant to figure out your tax implications.
[Additionally Added] I agree that it will be a challenging transition. But, in 10 years, this will be a non-issue.