Sounds like a so-called slime mold. Some go by the name dog vomit fungus. If so, won't damage your plants.

A quick google search for slime mold netted some pictures that look very similar to what I'm seeing. Would that explain the sudden need for extra watering? I will say the temp has been in the mid to upper 90's for most of the last week. Also, have two yellow squash plants within 3 feet of the zucchini which have no mold and do not need the extra watering.

Temperatures in ther 90's and plants growing in the hot sun can produce plants that wilt and may need extra water depending on how well the soil they are growing in retains moisture. That a slime mold is growing near this plant indicates there is some mulch around it which is a help, if the mulch is thick enough.
Look closely at the stems to be sure this one does not have a Squash Vine Borer.

Okay, so NOT a slime mold.

Perhaps southern blight? If so, not at all good.

I'm thinking now that it is indeed a squash vine borer. I'm going to slice open the stem tonight to look for larvae.

I'm not at all familiar with that critter -- we don't have it here, thank goodness.

But here's info & good images that might help.
http://en.wikibooks.org/wiki/Horticulture/Squash_Vine_Borer

Here is a link that might be useful: squash vine borer w/images damage