The language in the bill is quite easy to read.
Text of H.R.822 as Introduced in House: National Right-to-Carry Reciprocity Act of 2011 - U.S. Congress - OpenCongress
It plainly states that a state must have some kind of state issued permit for you to take advantage of this law. Most constitutional carry states have still retained their CC permit programs for reciprocity with other states so there is no problem there as you wouldn't be travelling without a CC from your state anyway right?
Someone from Florida please write this guy about the glaring deficiency with dealing with the 1000' from school zones rule in the Brady Bill that we all break without a permit from the states we are travelling in. I tried, but I can't since I'm not from that state, much less district.
https://stearns.house.gov/Forms/WriteYourRep/
Oh and ask for a response.
One must be wary of the mentality creating the problem or the law creating the crime.
I love America and the Constitution, if you don't then get out!