@rizzle, yes you definitely can! I called dozens of senators' offices asking if I could apply and hit tons of roadblocks. But eventually I got the call from Senator Reid's office telling me I got selected. And I live in Maryland! Neither of my senators were sponsoring pages, even though they are part of the majority party. Basically, keep trying and don't give up. You might get lucky through persistence.
For anyone wondering, my counselor spoke to the principal, the courses they offer are calculus, physics, government/history, and composition(english), and they have tutors for foreign languages. They're really flexible about making it work with your high school so that you're able to avoid any long term issues.