Let us know what happens.
Technically, drooping of foliage in any plant could be attributed to lack of water, but I think this is a little different. In every other plant I have seen wilt, the soil is obviously dry, and even a light watering perks the plant up in a matter of hours. My droopy daylilies never do this, and in fact, as you noted, in this case, the soil is not dry at all.
Here, I see this "floppage" in periods of warm, wet weather, or when there is an excess of nitrogen. I think it's a case of the daylily using its energy stores in response to various growth triggers, and the leaves are simply soft and new. Since the soil is still cool, it may be because the plant is outrunning the capabilities of its root system, much in the same way as spring chlorosis tends to show up when the soil is too cool for sufficient extraction of micronutrients. Rainfall is a fantastic growth activator, and, in a garden regularly watered with high-pH tap water, will lower the pH and release a lot of locked-up nutrients.
Either way, as several others have already said, this is nothing at all to worry about, unless you happen to have been feeding a little too much, or a bit prematurely, and in that case it's a signal to hold back on the nitrogen.
