I think I may have slightly mislead you. I was trying to get at the following:
on the Pi whilst it is running type:
'fdisk /dev/mmcblk0p' (assuming this is the SD card)
hit 'p' and check what filesystem is used for the second partition. Write down exactly what it says.
hit 'q' to exit and not harm your SD data.
hit 'p' - there should be only one partition, likely to be FAT32 or NTFS unless you've changed it already. Hit 'L' (I think) to get a list of FS codes and look for the one that matches the description for SD card partition 2, that you made a note of earlier.
Hit 't' then following the prompts, you need to enter the code. Hitting 'p' again should show the FS of the USB partition 1 is now a Linux one.
Hit 'w' to write the changes to card and exit.
Hit '?' at any point to get a list of what different letters mean, I may have got 'L' (lowercase BTW) and 't' backwards. Hit return after the letter or you get a very long wait.
'mke2fs -j /dev/sda1' this will format the USB drive to have the ext3 (somewhat safer) filesystem.
This will destroy any data on the USB drive!
'mkdir /mnt/USB' (unless you already have a prefered mount point).
'mount /dev/sda1 /mnt/USB'
Now, you need to check to see if /dev/mmcblk0p is mounted as /boot or similar. If it is, unmount it with 'umount /dev/mmcblk0p1'
'cp -a /[a-ln-zA-Z] /mnt/USB' (This copies, whilst keeping all permissions intact, the whole of the root filesystem to the USB drive. It misses out any directories beginning with m as you don't want to copy /mnt/USB to /mnt/USB, could get rather sticky. If there are other directories starting with m, copy them separately.
Now the complete content of the SD card's system is copied to USB. The filesystem is the same, the content is the same, the location is the only thing to have changed. Remount /boot if it was unmounted earlier - 'mount /dev/mmcblk0p1' and make the changes to the boot/kernel configuration files. You also need to make sure you are using the USB friendly kernel. All this just preps the USB drive.
All of the above is off the top of my head, so please read carefully and make sure I've not been an utter plum and typed anything stupid. Worst comes to the worst, just reformat everything.
This may be what you've tried, but you said you'd copied the image files to USB. That doesn't make any sense if you mean *.img, or the debian*.img (or whatever you use to flash the SD), or if you treated the USB drive as you treated the SD card. All wrong.