I did my update last night around 9:00 PM EST. The first took about 20 mins. When it finished, it asked me what country I was in (didn't have that option before) and one or two other questions before beginning a second update, which took about 40 mins. Those of you who have yet to go through it: Be aware that the bar will move almost imperceptibly for a LONG time. You'll think it's frozen, but it's not. Then it gets to about 1/3 along or halfway and moves much faster. At least, that's how it worked for me.
I think this has more to do with the servers being gangbanged than actual connection problems. I also was unable to connect to the VC store last night and got the error message. Things should level out as people finish updating their systems and log on in a more staggered fashion. Nintendo troubleshooting and improving server capacity will also help, of course.