One year my husband and I needed to put in a new fenceline. We'd had a drought for a couple of years and I was trying to use one of the lower pastures that was not as burned off from the heat.
I usually ran the tractor and he would guide the auger. We lined it up and tried to drill a post hole - only the very tip went into the ground. So my husband climbed on top of the auger, thinking it just needed a little push. The auger began to polish a little pock mark into the clay.
With the brakes locked on the tractor I got off and climbed onto the other side of the auger. It just polished the pock mark a little more.
We put the tractor up and set up a soaker hose along where we needed to put the fence posts. Left that running for two weeks and tried again. The pock mark increased to two inches deep and the wet clay stuck to everything - but the water had only made it to that two inch depth.
We never did get that fenceline in that year. The next summer after a couple of tropical storms came up into the NE Gulf we finally got enough rain to soak the ground so we could get into that clay.
Sometimes the only time you CAN dig is when the clay is wet!