I had a similar issue with my GTX 750 Ti. It's something to do with the drivers, not totally sure what exactly, but adding the GRUB flag nomodeset got me a TTY.
However, it messed up my GUI at the same time, so this solution may not work for everyone.
Solution - Add the nomodeset GRUB flag:
Open a terminal Ctrl+Alt+T
Enter sudo nano /etc/default/grub - You can replace nano with whatever your favorite text editor is.
Find the line starting with GRUB_CMDLINE_LINUX_DEFAULT and append nomodeset to its end. For example:
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash nomodeset"
Run sudo update-grub - this will make the above change take place.
Reboot - you should now have a working TTY.
If you reboot and your GUI is messed up, you'll have to remove the nomodeset flag, but that will most likely remove your ability to access a TTY - so you'll have to decide.
Messed up GUI - Remove nomodeset flag - It's exactly the opposite of adding it:
Open a terminal Ctrl+Alt+T
Enter sudo nano /etc/default/grub - You can replace nano with whatever your favorite text editor is.
Find the line starting with GRUB_CMDLINE_LINUX_DEFAULT and remove nomodeset from its end. For example:
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"
Run sudo update-grub - this will make the above change take place.
Reboot.