What exactly do you mean by ultimatums?
So, under the assumption that veteran DMs can adapt on the fly, let us say you are a newish DM, running a module. Said module includes an advancing orcish horde and a Duke whose domain is being advanced upon who doesn't have the resources to stop them. The PCs can stop them (with help perhaps). So far, so good. The module includes a variant on "The Negotiation" sample skill challenge in the DMG, where the PCs try to get varying levels of aid from the Duke (who will provide some level of aid regardless, but wants to keep the maximum military on home-defense rather than expeditionary duties). So far, I think a reasonable set-up.
Unfortunately, as the players discuss how to handle negotiations, you realize that it won't work: the players will demand a "successful skill challenge" level of support or they walk. They aren't interested in negotiation, and will treat repeated attempts to do so as a refusal. Out-of-game, you know they mean it.
So, the players have no intention of negotiating (i.e. participating in the skill challenge), BUT their offer is reasonable (an advancing, unstoppable without-their-aid orcish horde is a strong incentive). If they asked the impossible, or if they asked for the minimum, it would be easy: they short-cut to failure. Their request here is more problematic. You could say that the delivery was 1 diplomacy check (but the players are delivering their demands will all the diplomatic skill of a supermarket cashier telling you the total). You could say that the statement of "... or else we leave you to face the orcs alone" is a diplomacy or intimidate check (but the PCs aren't being duplicitous, and the Duke has a good Insight check). That gets you to 2 rolls, not enough.
More generally, in a negotiation, one party can always decide to put their foot down, say "final offer" and mean it (and no longer haggle). If their final offer is too high or too low, this poses no difficulties. If the final offer is marginal or reasonable, such ultimatums abort skill challenges without an obvious resolution.