So I've taken to doing 50 jack knife crunches and 50 sumo squats once a day every day (my original goal was 100, but it ain't happening, my muscles are burning after 50-60).

After two days of this I am SO stiff and sore, I have to lean on my chair back to sit down because my legs refuse to bend all the way.

Should I take a break? Should I push through? It's only 50 squats...it shouldn't be terribly taxing!

It would probably be best to give yourself a day inbetween - allow your muscles to heal a bit. Or possibly do the squats one day and the crunches the next and then alternate.

With strength training, and this is what you are doing, a rest day I between is good.