I use Carbon Copy Cloner to back up my smallish SSD to the internal hard drive about once a month (in Lion). I have difficulty unless 1) I boot into an old Snow Leopard disk and run CCC to back up the SSD (Lion) to the internal hard drive (also Lion) or 2) wipe the disk to which I'm backing up, at which CCC works just fine to make the copy. As I'm sure you already know, you need to boot from a disk other than the one you're going to try to fix (i.e. the backup disk). Never "upgraded" to Mountain Lion. Good luck.
BTW, using a 3.02 27" iMac (Oct. 2011, IIRC) running either the latest iteration of Lion or Snow Leopard (the latter if I have to use Carbon apps), w/ 16 gb memory.