There wouldn't be a single factor driving it but a combination of many factors. Loss of coastline (and cities built along it) including greater susceptibility to storms for unaffected areas will obviously have economic costs, highly increased weather and storm variability will be significant (think monsoon rains, "atmospheric river," etc.), increased drought in some areas due to both temperature and weather pattern changes (see western US water rights among the states as the civil portion of this), mass movements of refugees (sure the US can close the southern border, but what happens if you get 50,000 migrants all deciding to come over at once in one area? Are you simply going to shoot all of them?).
Human extinction seems very unlikely, but the collapse of the infrastructure that allows creation of the infrastructure that allows modern life? That could be much more likely, particularly when you factor in military conflicts as well as purely climate-based changes and losses.
It's quite hot around there. Wet bulb temperatures often near the edge of survivability outdoors.
It's worse now with 1-1.5C warming. If we don't stop, and we get to 3-5C warming, this could lead to large scale migration to Europe in pursuit of liveable climate. And warming won't stop unless we stop emitting greenhouse gases.
Seems vanishingly unlikely to me, on the face of it, but I admit I am not read up on all the possible doomsday scenarios.