This is an excellent topic because too much rain has presented problems for planting for many people lately. I know several people who are "holding" their plants in buckets of water waiting for better planting conditions. Planting daylilies that are already weakened from shipping into heavy clay soils can become disastrous IF the weather turns unseasonably hot and can result in the loss of the daylily.
There are some things that you can do 1) pot your plants in a good planting mix until they have recovered from shipping and then plant them later 2) work something "dry" into your soil before you plant to make your heavy clay soil drain better (baled peat or aged pine bark soil conditioners) 3) hold your plants with roots immersed in water. You can add a bit of Miracle Gro to the water if you like and the water should be changed every 3 or 4 days. Planting in "mud" should not be a problem in black soils that drain well during cool weather. But clay soils are just impossible to work with when they become saturated....my sympathies to those who have unimproved clay soils!