So how big of a sales tax would be required?  Juneau has a 5% sales tax and brings in $43 million spread across about 30,000 residents.  Expand that to the entire state and that brings in about $1 billion.  But it has a few problems:
1.  Juneau gets a million cruise tourists a year, so sales tax revenue is likely higher there than it would be elsewhere.  In reality the state sales tax would need to be 6% or more.
2.  Many out-of-state owned businesses skip town without remitting their taxes.  Difficult to enforce when the business is operating in the Virgin Islands or whatever winter cruise port.  It's a perennial problem there.
3.  A state sales tax would be piled on top of existing municipal sales taxes in the communities that have them (i.e. Juneau would have a 10% sales tax).  So they would have to switch to higher property taxes which the sales tax supporters would probably consider even less fair.

If you just gotta have a sales tax, make it a big one only in the summer season.