As long as the key in the link that the user clicks is the same as the one in the database.
Also for varchar, you have to supply a length for the field. If you have 32 characters, (eg md5 hash) you tell it 32. If you have 8 then you tell it 8. If you tell it nothing, then it will fail (as it did with you).
The alternative is probably better for you. Again the link that the user clicks must contain the same key that you have in the reset column - that will avoid you having to setup the column as unique.
My helpful sig has gone because a mod below the administrator gave me an infraction - despite the administrator personally agreeing to it.
If you need any php tips or tricks you can PM me.