with Sue; bare-root plants often need a bit of help to acclimate, but Karen, since yours are established plants that just need to be moved, they should be fine if the leaves are left intact. I'd dig with as much surrounding soil left undisturbed as possible, set the whole thing on your shovel blade and carefully drag it to its new home. This is the method I also use for moving huge chunks of hosta, and I successfully move them around all season long. They could almost be on my weed list here; they multiply like rabbits!
Seriously though; daylilies are tough plants. It's usually pretty difficult to make a fatal mistake. I've unintentionally left pieces in a wheelbarrow in the shade for weeks already...dealt with a crisis or two, and then returned to plant them...and they survived. Move them when you feel the time is right and I'm sure they'll be just fine.