I decided to create an iCloud backup of my phone & pad. Both devices are plugged into my iMac, and both can use the Wi-Fi that my iMac is connected to.
The first thing I did was go into iTunes, click on the iCloud button and press "Back Up Now". Both cases repeatedly backed up to my computer, even after rebooting.
Then I went into my iPhone, set it to back up to iCloud and repeatedly tried backing up, without it ever getting past the calculating stage.
Then I went to my iPad and tried the same thing. It asked me for my AppleID, which I entered, but it didn't accept. I switched to my iCloud password, and that worked. It started backing up. After a while it failed, and trying again had the back up work. I turned off iCloud Backup and checked in iTunes and saw the iCloud backup listed.
I never got a logon prompt with my iPhone, which is currently set to back up to the cloud. I don't want to leave it that way, as I don't want it starting sometime when I'm not in wi-fi range (my data plan is limited).