If there is a choice on the crisis card and one calls for someone to discard skill cards or pay some cost (such as Water Shortage where the President and Current Player descard 2 or 3 skill cards), but the cost is not able to be paid (if the current player only had 2 skill cards and needed to discard 3), can that choice still be made? (in this case, avoiding the loss of food).

Yes, choice can be made even if all conditions cannot be met

I agree with Toofy. I'd emphasize that this is different from costs, which must be paid (e.g., destination cards that allow you to risk a raptor or some other resource for a chance at a benefit, or Laura Roslin's discarding of two cards to activate a location), but you are permitted to choose an option on a crisis card even if not all its effects will occur.

From page 30 of the rules of play, top left corner under heading "Card Clarifications."

"Choice Crises: When a player makes a choice on a Crisis Card, he can always choose the top or bottom section of the card, regardless of whether he will be able to fulfill the game text listed (unless the card specifically restricts this)."

So I think they've hit the nail.

Yep, Water Shortage with the jump icon is about the best Crisis you can hope to draw...