Yes, it will be crazy busy. Monday is actually a slightly better day to go, as people are starting to fly back home. Today will suck. Tomorrow and Sunday will be terrible. I've had a Park City pass for about 15 years and learned to ski there about 40 years ago.
If you go, and if you're any kind of decent skier, get up to the higher, farther back mountains. On the Canyons side, get over to Super Condor, 9990, Dreamscape or Daybreak. The lines near the Red Pine Lodge will be terrible all day. Also, don't take the gondola from the Canyons base. Take the orange bubble.
On the old Park City side, try the McConkey's and Jupiter lifts. These are way in the back so they're not nearly as crowded. Usually. But they're all blacks and double blacks. Crescent, Payday, King Con, Silverlode, Motherlode and Thaynes will be packed. Sorry.
Come back in a week. It will be much nicer.