How can I recover Contacts from iCloud?

After accidentally deleting all my Contacts from my desktop, I recovered them in iCloud and exported what I thought was a backup Contacts Archive to an external drive. This backup shows all my Contacts as long as I'm connected to the cloud, but shows "No contacts" when I sign off from the cloud. I also tried to restore my Contacts from a December Time Machine backup, which asks me "are you sure you want to add 272 cards?" but when I hit the "Add" button nothing happens. Is there any way to get a copy of my Contacts from the cloud that can still be read when I sign off from the cloud, or is there any way to copy my contacts from my iPhone to my desktop without going through iCloud?