I am sorry to be the one to see your post first, and to tell you that your squash aren't wilting b/c of lack of water. Your squash have been attacked by squash borers.
At this stage, there's only one thing to do to salvage things-- one thing that I've found, that worked for me. Hope others chime in.
Do a search for squash borers to understand what happened. Briefly, a flying insect (the adult borer) has laid eggs on the base of the main stem (or others). When the eggs hatch into larva, the "worms" bore into the stem, and work-- that is eat-- their way up the xylem tissue. This is the tissue that transports water from the roots. So no amount of watering is going to repair that damaged tissue.
There are preventative things you can do, but too late right now.
If you do some research, you will see a bunch of what I consider hair-brained things to do at this stage, among them, trying to slit the stem with a knife and use tweezers to pull out the worm. Don't waste you time.
One thing you can do is go "upstream" of the worm, and try to root the stems. Any part of a stem that's on the ground-- and you can pull stems to the ground-- can be buried with soil (just an inch will do) & watered. That part of the stem will root, and thus be able to provide water to the leaves, and
flowers, beyond it. Keep the stems you're trying to root watered well, but not in a puddle.
At the same time, you can apply some Sevin dust to the stems close to the ground, including those you've buried. I hate using chemicals, and this is the only time I do, but I also hate loosing a whole crop of squash.
Sounds like you identified the problem today. In the days to come, you will loose many leaves-- they'll turn mushy & brown. Be sure to cut them out and dispose of them. If you don't, they will create an environment that will promote fungal growth, and your problems will multiply.
This happened to me last year b/c I wasn't paying attention. I had to rip out an entire crop of spaghetti squash, but did salvage banana, yellow and others. So there's hope.
Good luck!!