Pisa and Florence on one day - is it possible?

Yes, but you won't see much of Florence of Pisa. You can catch a train at Roma Termini that will get you to Pisa Centrale at 8:23 am. You can walk to the Leaning Tower in about 15 to 20 minutes and see some of Pisa along the way such as the Piazza dei Cavalieri. There's a regional train at 9:54 am that will get you to Firenze (Florence) at 11:07 am. You can leave Florence as late as 10:04 pm and get to Roma Termini station at 11:35 pm. http://www.trenitalia.com/ - for trains from Pisa to Florence select all trains to see the regionale trains; there are few fast trains on this route.

You can do Pisa in a day, but certainly not Florence.

You can, if you just want a stroll riverside the Arno, on both cities.
Pisa is quite a small town (in the Historic Centre) a couple of hours for a walkaround and other 2/4 for Piazza dei Miracoli, it depends how details lo look to.
Florense is an absolutely different fish to fry: the historical part is almosta a 2 mile circle and there are nearby places, as Fiesole and the "Ville Medicee" that can not be shunned.
In florence in one day only you can:
A) walk around and look at the "cenacolo d'ognissanti";
B) go to Fiesole;
C) visit the Uffizi and rest a little in Boboli
D) visit 2 of the other museum of the town, or the Academia.

The minimal period for a visit "OF" Florence, so you can have an idea of the town can be put in "a week" I put the places aforementioned in a step by step project: 1st day walk around and look at the "cenacolo d'ognissanti" I love it because it Was one of the first thing I visited with my wife; 2nd day go to Fiesole and Pratolino; 3rd visit the Uffizi and Boboli; 4th visit the Academia, 5th Bargello and Science museum, 6th last stroll: Michelangelo's house, San Miniato.
And of course there will be a lot of things to see more!

Rome to Florence is about 185 miles. Driving or a train, both means take a lot of time. Six to seven hours of this "one day" shall be on transportation. Are you saying to leave Rome early, spend 10:00 AM to 5:00 PM in Florence? Adding Pisa means more travel time. Less time visit either city.

Not quite except from the window of a train and a light snack at some restaurant. I suggest you flip a coin and choose one.

Pisa yes, Florence is difficult too see in one day only

I wouldn't bother with Pisa.