does the state then have the opportunity to collect a state tax along with the federal tax on sales and services that cross state lines?"
No more than they may already have authority to do. Most states now require their residents to pay use taxes on things they purchase out of state now, its just is not very feasible to enforce such provisions.
The FairTax legislation does not address the issue of state taxes on phone/mail/net ordered sales per-se.
If enactment of the "Streamlined Sales and Use Tax Act H. R. 3184" occurs, that becomes a more feasible scenario.
The FairTax legislation does seem to leave the door open for the states to make a compact to collect state sales taxes. That is if I'm reading section 402.c correctly.
(c) AGREEMENT WITH CONFORMING STATES- The Secretary is authorized to enter into and shall enter into an agreement among conforming States enabling conforming States to collect conforming State sales tax on sales made by sellers without a particular conforming State to a destination within that particular conforming State.
If enactment of the "Streamlined Sales and Use Tax Act H. R. 3184" occurs, that becomes a more feasible scenario.
As I read it, the stipulation that the states be "conforming" makes the FairTax legislation incompatible with the Streamlined Sales legislation because the states retain control of the definition of taxable property and services in the Streamlined Sales legislation.
I would like to see FairTax enacted and potential problems inherit with Streamlined Sales avoided (example).
If the (state-funded) forces working toward passage of Streamlined Sales could be convinced to work toward passage of FairTax, then both groups may gain.