Respectfully, the federal government only recognizes those Nations with whom they have signed treaties. It does not matter how large the Indigenous nation is, how organized it is. If at some point in the tribes past, the government wanted something from the Nation (like land) they recognized them and made treaties.
This is why it is very rare that any nation gains federal recognition now, the government already has the land - they don't need anything from us.
There were other immigrants that were sent to Carlisle Indian School - not because they were considered by the government to be "Indian" but because they did not know English, some of them were sent for an introduction to the language and culture. Attending Carlisle in no way implies that the government is recognizing someone as "Indian" There were non Indian immigrants that were sent there too.
Recognizing Tainos would not cause any change in the border of this country any more that Canada recognizing the Lakota people would change the southern Canadian border- that's not even a factor.
My point is, who needs the government to tell them who they are, and why spend such time chasing an elusive piece of paper? Federal recognition seems to me to be somewhat overrated anyway, and if your nation does not have a treaty with the gov, then you're not going to get recognition. But who cares if the Government knows who you are, it's more important that YOU know who you are.
I am of the same mind that I do not need to be told who I am, but here is my reasoning behind needing federal recognition. Even today it is very difficult, if not impossible, for a non-recognized tribe to have the religious freedoms that most people take for granted. Here is a prime example: http://www.winnememwintu.us/ this California tribe had their recognition stripped from them without even being at the table. So now they want to perform a sacred coming of age ceremony for one of their women, are being ingnore because they no longer have that recognition. Or the blocking of the Taino people access to the sacred ceremonial grounds of Caguana. Is this a guarantee? Nope, but the tribe has a little (and I mean a little) more clout. Otherwise, unless an apocolypse happens, I doubt we will ever see recognition. Especially since most people really do think we are extinct. JMHO.