I've always thought that in X1, since Jean Gret was debating Kelly and Xavier was in the public, I assumed that the world knows about Xavier's school and that's why parents are dropping their mutant kids there.
And in X2, the President acts all surprised when they see the jet. Oh, maybe he didn't know Xavier's underground base, likely.
Did the government not know anything about Xavier's school? Isn't it a public school to welcome mutant students?
I'd say, the government knows about Xavier's school, but doesn't know his underground base. Maybe they gave him the money.