Saline Valley Road is in great shape, except for a stretch (maybe 100 yards long) of soft sand and another bumpy "small boulder field". The only real problem a car would have is on the spur road. There are some pretty deep wash-outs in the first section. I personally wouldn't want to take my car through there. But we did see some cars out there this past weekend. Somehow they did make it through.
Another option is riding with someone else. Maybe there's someone else that wants to split gas money? At the very least, if you drive your sedan I would suggest convoying with other SUVs or trucks just for safety's sake. Also, a shovel can go a long way in helping to get you through any rough spots in the road.
One final word of caution, the weather is apt to change the condition of the road at any time. There could be wash-outs or snow. The South Pass is about 6,200 feet, so in the winter, storms often leave snow in the pass and it could become unpassable for at least a few days (or longer). It would be advisable to bring extra food and let someone know where you are because you can't make phone calls from out there to tell them you won't be getting home on time! (A couple of years ago there were 10-15 foot drifts in south pass!) Even tire chains couldn't get a vehicle through the pass then. But bring them just in case.
If you have any other questions I would be happy to answer them.