Such an ultimatum can be private, "Exile or death," in the sense of a simple statement to Mr. Assad that it is foreseeable as a consequence of his regime's actions that if he does not make a credible move towards exile and some reasonable peace plan as part of that, without him however as he has no more credibility left, then he will be like Muammar Gaddafi: dead.
On the other hand, there is no reason to have nitpicking lawyers get a lot of people killed arguing over fine points of international law as to getting his fanny out of the country and into exile.
As to why the Great Powers shouldn't object to such an ultimatum, Russian contracts and interests have been respected before in such matters, as to their braying about things, and China will do nothing without Russia.
As to their objections, on the surface, and below it, Syria's not a good candidate for democracy, to be honest. Neither were Bosnia, Serbia or Kosovo, and if there are difficulties there still, it beats what happened before NATO intervention, and by a large margin.
That's something Bill Clinton is proud of for good reason, just like Rwanda is something that bothers him to this day, as to the idealistic case for an ulimatum to Hafiz al Assad that his time has come and gone.
As to the risks in Syria and democracy, who is a good candidate for democracy at some point in their history?
It's still how we roll, and we also don't stand still while an army shells urban areas, not at least without a pretty darn serious statement, Russia be damned if need be, unless that little doggie thinks it can be the Big Dog, and then we have to fight about it, and see who's the Big Dog.
Otherwise, we respect Russian interests as usual, and even help them as to reconstruction and pipeline development Syria, the region, and broader world would all benefit from right now, Russia too.
Nonetheless, in terms of our ideals, tens of thousands of lives are at stake for our ideals in Syria, if they will be imperfect bearers of those ideals for sure.
They're Muslims, they're pretty hard core about that more than likely in a lot of cases, and they don't have any experience running a government, not to mention a hint of a democratic one, hence a lot of people supporting Bashar Al Assad's butchery by looking away.
There was a time when Bashar al Assad raised hopes in people, like Saif Gaddafi in Libya, or Gemal Mubarak in Egypt.
That's not how family businesses often work out, especially political ones, for all sorts of reasons.
In the case of Bashar al Assad, we know from the experience of his reform efforts in 2001-02, that his Dad Hafiz al Assad constructed, like Saddam Hussein, a brittle nightmare of a state that can brook minimal opposition, before it has to call in the airstrikes and artillery, like at Hama in '82, or Homs now, wherever.
That's how the Syrian military has learned to obey its masters, which is an argument for demonstrating we won't tolerate that past a certain point they crossed over a long time ago.
That Syrian military's approach to domestic dispute resolution is a demonstrable fact, the real question being, what are you going to do about it, especially if Russia objects?
China won't take one step without the Bears.
Well, as to self-interest on top of ideals, since we have to face down Iran anyway with Iran to very serious point, we might as well see if Russia really think it's a good day to die, like Sitting Bull said before attacking Custer, our self-interest in a simple ultimatum to Bashar al Assad: Exile or Death, which will you?