LostSoul said:
Let's say we have a skill challenge in a game. It's "Convince the King to send troops to the Keep on the Borderlands."
One of the players rolls a success with Diplomacy - let's say it's the 2nd one out of 6 needed - and says, in character, "If you don't do this, we will never work for you again. We'll leave your lands, and you can pick up the pieces." The other players have their PCs nod in agreement.
The DM thinks this statement would have a huge effect on the King, so he says, "You know what, guys? The King gives in to your demands. He needs your support that badly. You win the skill challenge."
I think the skill challenge system needs something like that.
Your set up doesn't sound a lot like a skill challenge to me. The challenge should involve more than a few diplomacy checks. You can have situations like this, but they should probably be solved through RP or with RP and diplomacy checks.
I also have to say that giving ultimatums to the king is usually frowned on. In some cultures it could get you killed or imprisoned. Any king who gave into ultimatums would likely be viewed as weak and ineffectual by his court. Players in my upcoming 4e campaign would be wise to remember that King Goran Drago came to power at the age of 14 by engineering a palace coup, slaughtering the regency council and purging the Druidic Church of his opposition. It would be unwise to attempt to bully him in this fashion.
As for skill challenges, I think it will be necessary for the GM to be careful in how he constructs them. Just like encounters, a skill challenge should be designed to be interesting, challenging and fun. In the example above, the challenge would likely include:
1) Discovering the correct way to approach the king
2) Getting in to see the King
3) Convincing the King of the need for troops
4a) Convincing the military advisor to send troops
4b) OR, convincing the King to overrule his military advisor
If the King's advisors are in the room (likely at most courts), they may concerns (real, imagined or a cover for plots of their own) that could lead to them arguing against the PCs. Perhaps History, Local or Insight could give the party an idea why the advisor is arguing against sending troops. Intimidate (to make him back down), Bluff (to make him think that they know something he wouldn't want revealed), Diplomacy to ease his fears or to get better cooperation could all be useful in these circumstances.
I've said that I'm not a big fan of the X successes before Y failures approach. I've always been able to wing encounters of this sort without a system per se. But I can see that it could be helpful to GMs who aren't experienced, who aren't comfortable winging it or who like to have a mechanical system in place to provide a framework for social encounters.
To me, the best thing about this system is that it could lead to solutions the GM didn't think of ahead of time.