This is why they added a Companion Terminal to New Vegas.
You can try recruiting Dogmeat, then killing him. That should free up a slot so you can hire another follower. You can ressurect Dogmeat, hire him again, then kill him again to get multiple followers.
Ok, so after many hours of research, I found what was causing the problem, and even the Companion Terminal wouldn't have helped is it was in Fallout 3.
It's funny that you mention this Dogmeat trick to have multiple followers, because it is indirectly part of the glitch.
So, with Broken Steel, a perk called
Puppies! was added to the game, which makes spawn a new Dogmeat when he dies, pretty cool, huh ? Except their way to deal with the multiple followers trick is to set you follower count to 1 (meaning the game will consider you already have one) every time a puppy Dogmeat spawns to replace a dead one, which is why I couldn't hire Clover or any other companion.
Since the perk, here's what I did :
I typed in the console "player.removeperk 02003211" to get rid of the perk which was causing the glitch (02003211 is the id fo the perk, but the first two digits might be different depending on your region and which expansions you've installed).
Then I killed Dogmeat (using "prid 6a775" to target him, and then "kill"), which reset my follower counter to 0, for some reason, and allowed me to rehire Clover.
Finally, I took back the
Puppies! perk with "player.addperk 02003211" and everithing went back to normal.
So basically, if you have the
Puppies! perk and Dogmeat dies and respawns while you don't have any other follower, it will prevent you from ever hiring one again unless you do what I just explained.
Edit : Is it possible to add "[Resolved]" to the title of this topic ?