Tourist do pay taxes. Hotels and cruise ships charge a head/room tax already to help offset the expense.

Out of state workers are very well compensated, that's why they come here to work. Plus, they don't have to pay taxes on top of it. Maybe this will de-incentivize them to come and take Alaskan jobs and will help with the unemployment rate here. 

A state income tax will also help close the loophole in Alaska as being a tax shelter for the rich so they don't have to pay them in their state. I'm guessing that's why we are seeing such a well orchestrated campaign to not enact one.