I'm gonna guess that the dude would be fine. Assuming that there is still an infinitesimally small space still between each portal/wall, and since there is now an infinite amount of portals, the dude would really be in an infinitely long tube and not be squished.
from the perspective of the world looking at the portals/person
portals don't actually contain any space in them, they're more like a mirror
once there's a portal on both of your arms, your arms would be touching eachother
if they go any farther, you start getting squished by yourself
from the perspective of the person
as the portals close in, the other yous also close in
there are an infinite number of other yous, but the infinite amount of space going forward is shrinking
so the ratio of yous per space is still getting too small and you get squished