Unfortunately this is not a new tax. There has been an "obligation" to pay tax on purchases from out of state (online, catalog, etc) for sometime. I just don't know of anyone who have volunteered to do so. States have been whining about making sellers bear the burden of collecting taxes for states that they do not even reside in (but are selling to) for quite a while now. They would want it automated even if people were sending it in, though. Just as with the Income Tax, the more automatically it happens, the less people are aware of how much they are being taxed.
If you are Amazon, maybe you can absorb the costs (or pass them on) easier but if you have a small family business selling custom gun parts nationally, for example, it can be quite prohibitive/costly to have to keep up with 50 states + our territories' tax structures as well as collect and file everything. It's the overhead of keeping up with all of this that will hurt businesses (especially small businesses).
See below for TN state website info on personal responsibility to pay for online purchases:
Sales and Use Tax Frequently Asked Questions
Consumer Use Tax