You mean, "accept our refugees or we all die together" doesn't work?
You would have to have a government that is simultaneously actively advocating its citizens to abandon the nation while also threatening a nuclear strike on a neighboring nation and drawing the ire of the rest of the world.
Think of it like this: Developed nations caused our land to be uninhabitable, so we move to their's. If they don't accept us, we make their land uninhabitable too.