I thought I'd relay an answer to a rule question I just got from Corey Konieczka:
My question:
Concerning Laura Roslin's disadvantage: can she activate locations when she does not have at least two cards in her hand? Or does she simply discard the rest ("rest" also including zero cards)? Can she continue to activate locations when she runs out of cards?
His answer:
No. Laura Roslin may not activate a location unless she has the 2 cards to discard.
I hope that this answers your question!
-Corey Konieczka
Fantasy Flight Games
Design and Development