You should be able to find a spot on a Thursday. Friday or Saturday, not so much.
I would go a little further north, and stay at Boyd Lake State Park. Bigger campground, and not right off the interstate, so there won't be nearly as much auto noise.
2012 RAM 3500 Laramie Longhorn DRW CC 4x4 Max Tow, Cummins HO, 60 gallon RDS aux fuel tank, Reese 18k Elite hitch
2003 Dodge Ram 3500 QC SB 4x4 Cummins HO NV5600 with Smarty JR, Jacobs EB (sold)
2002 Gulf Stream Sea Hawk 29FRB with Honda EV6010