I had the same problem, as have others, I'm sure.
The nut should sit in the plastic (the frame for the heated bed). I'm pretty sure the spindle has another nut, or perhaps a stopper, at its top. The nut you are referring to is designed to hold the spindle in place, to stop it from spinning.
You can get the nut back into place by keeping it fixed in one position, with a screwdriver or pair of pliers, as you mention, and turn the spindle by hand, until it is pulled back into place.
Getting it to stay there and prevent it from coming loose again is another matter. I wrapped a cloth around the spindle (to protect it), and gave it a few sharp turns with a pair of pliers, which seems to have done the trick for now. I would suggest not being over-zealous when doing this, in case you crack the frame, which will create a whole new problem for you...
I have read that others have glued them into place with super glue, to stop them from coming loose again (once the nut has been re-seated in the plastic). This appears to work well.
I've been trying to come up with a better idea, or a mod to fix this, but have had no luck so far.
My idea will work as an interim measure, but no doubt the spindle will work itself loose again sooner or later, so super glue may be the way to go.
Cheers,
Jeff