I know I've already rephrased this two or three times already, but one more time.
Imagine Obama was a real Hostage Negotiator. He refuses to deal with the hostage takers, until the hostage takers harm one of the hostages, which makes Obama cave immediately. What do you think will happen in the next hostage crisis? The next hostage takers will know exactly what to do to make Obama give in, and just skip to harming the hostages for no reason.
Obama didn't just lose this crisis, he created a whole range of new artificial crises.