I don't think that such well established government structures would collapse as such. There is a lot of tradition and systems in place to keep tings going. What I would expect is radicalization though. The nations will be facing more and more pressures. As it was mentioned already, there would be a lot of refugees to deal with. There will be increase in poverty and from that increase in tensions between various groups, likely spurned on by the upper classes in order to keep the rabble occupied. The power centers will retain their standard of living for a good long time, if necessary by taking away the resources from the periphery. The periphery in turn, however one might define it in any specific case, will deteriorate at a faster pace, creating subcultures in extreme poverty, no go zones or even actual wastelands. Also, as others have mentioned already, the current power centers like US, China or EU will each have their own unique path, based on their current policies and cultures, as well as their geographic situations.
I had often thought you could write a Pearl Buck type story where the affluent are wiped out along both coast in the US and a new shoreline would be created. Maybe combine two of her books ...The Big Wave ...and.... The Good Earth ... Hopefully the new shoreline would reach my house and I would have a waterfront view. It's only ten blocks. One could hope.
Keep in mind though that, in most advanced economies, the population is aging and shrinking. US fertility rate is 1.64, well below the population replacement value of 2.1. Global population will peak at around 11 billion towards the end of the century, so the demand for resources will peak as well. Water desalination requires power, and with fusion looking like it might be viable (despite arguments about whether it's a good solution), that can be overcome. Food is actually not, in itself a problem. There's enough food, it's mainly a problem of distribution, getting the food to where it needs to be. Living space is really not the issue that some make it up to be. Countries like the US have large areas of empty spaces, although obviously, living space competes with agriculture and nature. The main question is what to do with cities that are in danger of being submerged. London, for example, would be very vulnerable, but some people would say London sinking wouldn't be a bad thing.
I think Robin Williams said it best. "Remember the great quack of 84, when everyone in California surfed to Denver."
Like JT, I say look no further than Katrina. Water ain't no scarcity, finding and keeping it drinkable is. We already know that a crisis breaks down transportation and distribution. I plan on writing these circumstances into my story cause - good drama! We need to learn all these hard lessons again so we can teach our children to forget them, too. Displacement happens without natural stimulus. Look at the California Mass Exodus in the early 90s. The scarcity apocalypse will be on us when the scarcity is us. We're too many generations informed about the One Percent, so they'll be first on Bastille Day - likely because they don't really have anything we can eat. Then politicians will flee! It's really about how we fall apart, cause scarcity is already here. Delicious drama! The irony is that reality is now a writer's wet dream! There are too many unstable structures, and people, to eliminate the coming threats, so I guess I'll have to focus on what's first. O_0 So, to the OP, yes.