Welcome to "just crazy". In 2003, my husband and I had the same circumstances. We were not planning on going south of Orvieto, but when we realized we were a short train ride away from Rome, we couldn't resist. We changed some things around and "eked" out one full day for Rome. To complicate matters, the day we could come was some "special" day. Every site was free, which meant huge crowds .While it has been a long time since then, I think it can still be done. Europe is probably busier now than it was 2 years after 9/11...but the "special day" made that particular day quite busy. We had an amazing time and have never had any regrets. I have been asked, chastised, inquired by people: Why didn't you stay longer? Was it worth it? etc. My reply: We may have only had one day in Rome, but it was an awesome, fun day and well worth it.
What we did:
If you only have one day, it has to be well planned out. We were staying near Orvieto, so we caught the earliest train to Rome that we could. We immediately bought 24 hour transportation passes and used the metro and walking to get around (The metro is limited, but is good to get from the one major site to the other) We were at St. Peter's and in line when it opened. Then we went to the Vatican museum. Because of the free day, it was packed. We really just wanted to the see the Sistine Chapel, but you couldn't even walk through the museum. Fortunately, a private tour guide was able to talk to the guards, and they took down some ropes and let her couple through. Since she had been visiting with us, she let us tag along to the chapel. My journal shows we left the museum about noon.
We rode the metro to the Spagna stop and got off. After a quick lunch at McDonalds (Eating quick was part of the plan) we visited the Spanish Steps. Then we bought a gelato and ate it on our way to Trevi Fountain. After seeing the fountain, we walked back up to the Metro and rode it to the Coliseum. Coming up from the Metro and seeing it for the first time was a real wow moment. After visiting it, we walked across to the Forum and explored that area. We spent most of the afternoon in this area. We walked out of the Forum area by the Emmanuel monument. We walked from there to the Pantheon exploring the area and seeing the sites between including Trajan's column. After visiting the Pantheon, we walked back by Trevi Fountain and then took the Metro back to the train station. We were back to Orvieto by 9:00 PM.
Some advice:
One of the hardest things to go through in a timely manner will be the Vatican museum. You might consider trying to arrange a guided tour of that it either first thing in the morning or last thing at night. Then you could do the rest on your own and at your own pace. Also, know what you want to see in the museum and let the guide know. Due to the crowds, the only thing we saw was the Sistine chapel, but we were OK with that.
Prepare, prepare, prepare. Ir you really want to see all these sites, you have to have an idea of when you need to be moving on, the operating hours of each site, and have the order laid out. This was the one day of that trip that we knew exactly what we were going to be doing when. We knew which Metro stops we needed for each site and located them on a map (this was before we had a GPS on our cell phone).
As I said earlier, with one day something had to be sacrificed. We chose food. Other than our quick stop at McDonalds, we did not eat any meals in Rome. (We ate breakfast and dinner on the train. (yogurt, fruit, granola bears, a sandwich, nothing fancy)
Overall, we felt like we enough time at each site. We actually finished earlier that we had to, which left time for the relaxing walk back through the heart of Rome (Pantheon, Trevi, etc). We returned to Rome in 2008 and spent several days there. While we had more time, I am not sure we had more fun. There was something about that one day "blitz" tour that was just so enjoyable.