The tax will restrict competition. Today, people have a choice between online and physical retailers. Physical retailers know that a person can enter their shop, whip out their mobile device and order the same product online. That threat forces them to figure out better and ingenious ways to service their customers. It also puts downward pressure on all prices, making costs cheaper for consumers. Increasing the tax will put some retailers out of business limiting consumer choice.
American GDP will drop because increased taxes will cause people to buy less. That will lead to less job creation and less economic activity. An internet tax could cause unemployment to rise.