That's an actual sales strategy. I studied it in one of my psychology classes in college. There's a technique called "foot in the door" -- more formally, a type of sequential request. You ask for something small, and if it's granted, ask for something slightly larger, then larger still.
For example, someone comes to your door and asks you to sign a petition in favor of better health insurance for everyone. It's a simple request, and a popular idea, so you sign. Then the person asks if you wouldn't mind putting up a sign in support of the idea in your yard, then asks for a small donation, then asks you to circulate a petition of your own door to door, etc. Once people start agreeing, they can begin to feel like suddenly saying no would be letting the cause down, even turning against their own ideals. It has a proven effect.
PETA is doing the opposite of that, which is also a fairly well-documented technique. (Whether they're doing it deliberately or not, I can't comment.) In that case, you begin with the most outrageous request possible.
"Excuse me, sir. I see you have a bumper sticker in support of the giant panda. Would you donate your entire net worth to save them?"
"In that case, would you subscribe to our newsletter? Only twenty dollars a year, and all profits go to help the giant panda."
"[sighing in relief] Oh, yes, of course I'll do that."
You do have to be careful with that technique, of course, because it is awfully easy to end up looking crazed. But if you're talking to people already in favor of your cause, it can be effective, used sparingly.