Hi there, Laura -
Yep, the standard advice is not to try and cram in too much. There are many good reasons for this, including the flex to work around weather, unexpected transport snags, closed attractions on the one day allowed for city ___, and the time it takes to physically pack up and move to a next location.
That last point is really important as it's usually the most underestimated. Packing up, checking out, getting to stations, waiting for trains, sitting ON the trains, finding the hotel, checking in (or dropping luggage if it's too early to do so), unpacking....figure the process for each move is going to eat at least half a day of the very few days you have to begin with.
2 nights in any city = only 1 full day of sightseeing. No, you don't have time for a Tuscany day trip if you want to do any justice to Florence itself but maybe you're not all that interested in the attractions there?
Additonally, it's very likely going to be brutally hot in most, and very busy in all, of your listed locations. IMHO, one of the best ways I know to get a negative impression of Rome, Florence and Venice is to try and sightsee the top attractions with very limited time. You end up smack in the middle of the biggest tourist masses ALL day, and that can get real old in a fat hurry. Add summer heat and humidity to that and it's a recipe for exhaustion versus fun.
Also, where are you flying home from? You'll want to place that city at the END of your trip.
Sample itinerary with the 8 nights you have (and it's tighter than I'd personally enjoy):
Night 1 - arrive Venice (partial day)
Night 2 - Venice
Night 3 - Florence (partial day; transfer from Venice )
Night 4 - Florence
Night 5 - Florence - day trip day
Night 6: Rome (partial day; transfer from Florence)
Night 7: Rome
Night 8: Rome
Next day: fly home from Rome
If it were me? I'd drop Venice and stick to Florence and Rome, depending on your specific sightseeing interests.