I read a lot of these Migration-Assistant-hanging threads for a while looking for help, and I just wanted to note here on macrumors what ultimately worked for me.
I was migrating from a Mac Mini to Mac Pro, both with Intel chips. I attempted it with an Ethernet connection between the two computers. With about a half hour left, the Mac Pro told me the Mac Mini was not responding. I clicked Cancel, and Migration Assistant got hung up on the message "One minute remaining" during the Cancel process. I left it that way for 12 hours and then called AppleCare.
After confirming that I had no menus at the top of the screen to use to Quit (because this had launched during setup, before I had ever gotten to the desktop), and trying Command-Option Escape without success, they told me to power down the Mac Pro by holding down the Power key for 5-10 seconds. They recommended migrating from my last Time Machine backup, and recommended again connecting the Time Capsule to the Mac Pro with either USB or EtherNet cable--not doing it wirelessly. I did this, and I was able to "complete" a migration successfully. But at this point, things were pretty messy on the Mac Pro drive. There were a couple of extra accounts and I had been forced to give my own admin account a name I didn't like. A lot of my music and movies had transferred during the initial, aborted migration, but I wasn't sure that all of it had and it wasn't located in the right account anyway.
So I used Disk Utility to erase the Mac Pro drive and ran through Migration Assistant again, this time using the Ethernet-connected Time Capsule from the start. That seems to have worked quite well.
One final note on this. The Migration Assistant that launches automatically during the setup process for a brand new drive has difficulty recognizing a Time Capsule hooked up through Ethernet. The AppleCare rep told me this is a known issue. So one has to click on the "No thanks, I'll transfer my data later" button, get through the setup, and then launch Migration Assistant from the desktop. Then it finds the Time Capsule no problem.
Hope this helps.