How can I back up my iMac from the Recovery Partition? Things in my iMac are failing, most notably the hard drive. I can only reliably boot to the Recovery Partition. Booting to the regular system, either normally or in Safe Mode, does not work, and causes the machine to power off midway through boot. 

This computer is most likely fubarred. Is it possible to initiate a backup through the Recovery console? I'd prefer to get a Time Machine update, but I'll take whatever backup I can get.

I am running the latest version of Lion (OS X 10.7).
Unfortunately you cannot backup the Mac through the recovery partition. However starting the Mac in Target disk mode or booting the Mac from a bootable external drive may allow you to mount the iMac's drive and copy files from it.