If it's a federal tax, it will hit the ecommerce sites at a time when many are already hurting. If they try to allow the states to apply their own different tax rates would drive most online retailers out of business, as the accounting costs would be ridiculous.
It's the latter, sorry. If I read the bill correctly, retailers would be responsible for charging and sending (don't know the interval) the withheld sales taes to the correct states.
Technically, this changes the burden, since technically every individual is supposed to pay to their state the sales tax on items purchased without sales tax in other states (e.g. Online). Thats why Pols are saying this is enforcement--since the people refuse to do it (compliance is less than 12-14%), shift the burden to the retailer, as with POS transactions. It's still dumb, but that's the legal excuse.
The problem is it federally reduces the ability of states to compete among each other for businesses--right now, since it's only the retailer burden if they have a physical presence in the same state as the purchaser, a retailer can chose a state with fewer people (fewer orders) and/or lower sales tax (reducing the burden for those that do order). This stupid law will just (as you said) increase accounting costs on the businesses, which will ripple down to consumers. A side effect will be it will allow states to compete for residents more effectively (MT and DE for example), but that positive will be small compared to the overall negative.
The funny thing is, technically we are all breaking the law ordering online and not paying sales tax...but rather than pols realizing that as a sign, or even trying to enforce it, (un popular with all voters) they do this (unpopular only with smart voters).
The question is, why don't they put the requirement on CC companies instead of the retailer? They have the infrastructure to do it easily, and they already have the data--if the transaction doesn't have sales tax included, the CC company adds it based on the card holders residence (which they have). I'm not advocating that, but it seems simpler and less disruptive to businesses of all sizes. (less bad than the current proposal).
The ideal would be to suck it up and let the states deal with it, rather than the high spending states (the ones advocating this) with high sales taxes forcing the rest of the states to enforce THEIR rules.