For how long has it been stuck at 1 minute remaining? If it becomes clear it's not going to finish, your only option is to do a hard shutdown by holding in the power button of the target computer until it shuts down. After that, I would go back to the source computer and run Disk Utiity Permissions Repair from a Safe Boot--Shift at the startup chime--expect a much longer time to boot. The Safe Boot will check and if necessary repair the drive directory and also clear some caches.
Then boot back normally on the source and go to Sys Prefs>Energy Saver and make sure everything except display sleep is set to never, and also uncheck Put the hard disks to sleep when possible, if it's checked.
If that doesn't help, then there might be a corrupt file somewhere that's hanging the transfer and probably your only option if that's the case, is to bring things over manually.
What were you bringing over? Did you select everything?
Don't know if it will be necessary to erase and reformat the drive on the target computer before trying again. Might not hurt to do that now, but perhaps someone else can advise.
Also, was this the first boot of the new Mac, if a new Mac is involved?
Message was edited by: WZZZ
Also, if this was the first boot a new Mac and you were using Setup Assistant (many call it Migration Assistant), which only appears on the first boot, see this article by Pondini about how to get a second chance at that, as well as general information about transferring.
The timing calculation is widely inaccurate.
I'm tranferring about a TB of data from my old desktop, and it's been stuck in "less than a minute left" for hours now.
Luckily if you've enabled remote access (ssh) you can login and run nettop to see what's going on.
The counters are persistent per session so you can see total bytes transferred over the entire session.
Apparently it has done about 400GB in 18 hours or so and it keeps sending data.
Now I know it's gonna take at least that long to transfer the remaining data.
This is 1G ethernet connection, both desktops connected to the same switch (apple air express).
There's a lot of small files that is not helping either.
It would probably do better with an archive.
I've got the same problem. My new 3TB 27" iMac with all the bells and whistles has been freezing under completely random circumstances. Early this week the screen went completely black while I was watching a YouTube video followed by "the grey screen of near death" so I took it to the Apple store. I picked it up today and was told they couldn't find any problems but reformated the hard drive and reinstalled Mac OSX 10.9.2. I brought it home and started restoring my disk load from a tested cloned copy of the original. It indicated that the transfer would take 5 hours (USB drive, since my Seagate Thunderbolt drive died two weeks ago). After only about an hour the "Less than a minute remaining" message was displayed and it's been displayed for the last 5 hours. The ball is still spinning! Shall I stop and start over or just let it go?
In the end I did a Time Machine back up and transferred the back up to the new Mac. It went much more quickly than I expected. When I finished it told me that it hadn't transferred an application that was incompatible but everything else was there. Bootiful!
Why it couldn't have done that transferring Mac to Mac I don't know.