What does the Constitution say about the matter?

Quill vs. North Dakota, is the case on which the Amazon suit focus, however there is one area of the Constitution being cited by Amazon in it's suit against New York.  This is the equal protection clause. Based on the public comments in the legislature where they have dubbed this the "Amazon tax law" it appears to be an open attempt to specifically target one company for special "consideration" in damanding they collect taxes for the state.  It appears on it's face to be an open violaton of the equal protection clause.

Obvously this specific situation was not conceived of by the framers of the Constitution. Only modern technology has made this mess possible. In the "old days" the only place you had to shop were your home town stores. Sears catalogs and sales were, back then, typically delt with via a local store owner. No one place phone or internet orders across state lines.

The Constitution does address interstate commerce and gives to Congress the right to regulate trade between and across state's borders.

This would be a situation ripe for Congress to step in and set some ground rules to protect all citizens from the whims of an individual state.  After all it is the responsability of each state to collect it's own taxes. It is not the job of private business in another state to do their job for them just because they can't collect from their own citizens.