They are going to lose a lot of money.
Not likely. People aren't shopping there because there's no sales tax. They shop there because the prices are lower than bricks and mortar stores, it is convenient to shop (never closes, and I can buy whatever I want from my iPad sitting on my couch), and if you're a Prime member, everything comes with two day shipping.
Viola! New lawnmower, delivered right to my door in two days--for free--and I never have to leave the house. I don't have to drive to the mall, I don't have to worry about whether the box will fit in my car, I don't have to worry about getting my kids together. And Amazon does all that for less than the price of what I can buy it for at Lowes.
Sales tax? Pfft. Who cares?