is one day in Rome possible

If you have a specific area of Rome of interest (the Vatican, or the Forum, or the Borghese, or some other discrete area), I think it's definitely worth a day trip, provided you can get an early start. Getting around can take a fair amount of time, which is why I'd suggest one focus. You might also think about pre-booking a walking tour in an area of interest. I've been very pleased in several experiences with Context Rome (provided you would be interested in a small group, focused on learning instead of entertainment, academic... I think Rick Steves described them as tours for people with long attention spans); you could check out their web site.

There's a new ES*Fast train that gets you from Pisa Centrale to Roma Termini in 2.5 hours, making a day trip easier. I agree with Sherry, you'll need to focus your sightseeing. Choose either historic sights or Vatican for this visit, and then toss a coin in the Trevi fountain to ensure you'll return someday to see more.

This is where the hop on/off buses works very well. It will provide a good overview of the city and you can decide which site you want to spend extra time at and the bus provides convenient transportation. The on/off buses start right across from the train station.