My buddy made it years ago in the same model. Then again, that car was abused and is in the junk yard now. You can at least get down the initial hill to the Green River and a few more miles to the turn off. One significant hill climb and descent is in the way, but a few years ago a car could make it if it had the traction (sandy silt).
Was in there last weekend. I've got a pretty burly truck and didn't go all the way to the campsite. There've been some big rains and the riverbed/road is full of big rocks. It's an easy hike in the riverbed so a few mile approach is not a big deal. F'in' hot last weeked. This weekend looks WAY better.