Are you using a non-widescreen display? The wiki says sometimes you can't see it on non-widescreen.
* The left side of the console might not be visible if you are not using a widescreen display. In this case, type several tabs to move the cursor in before entering your commands. They will still work.
OR
* Go into your Fallout New Vegas install directory, find Fallout_default.ini (make sure it is not read-only) and open it in notepad. Then use ctrl+f to find the iConsoleTextXPos line and change the 30 to a larger number, 200 for example. This will make the console appear in the right place.