Earlier quoted context omitted.
Why would civilization be over? The sea rise wouldn't happen over night and people would move or build walls.
That's a lot of people to move and things to rebuild. Op did say "the current round of civilization". I also agree that lots of things changing at once are likely to create instability, with negative economic and social impacts (unless governments massively intervene, which I suspect many in the US would not appreciate). I'm sure walls are an option, but they will be expensive to maintain and it doesn't take much to…
If that's the bar for civilization ending, then civilization ended when people came to the US, ended again when they expanded out to the West, etc.
Just because people on the US coasts move means little to the 60 percent of citizens that don't live near the ocean.
And again, it's not going to happen overnight. A wall of water isn't coming in that will force everyone to put their things in a car and go. It will be slow build-up that slowly forces people out as they decide it's to expensive to mitigate.