To be honest, I love Italy but I'm not a big fan of those style tours because the amount of time in each area is very limited. However, I can appreciate that if you're on the tight North America work schedule (2-4 weeks of vacation per year) that some sacrifices have to be made.
I've been maybe 6-7 times to Italy over the last 2-3 years.
4 days in Rome isn't a lot, 4 days in Florence (FI-SI area of Tuscany) is a tiny amount (more time is need here than Rome) and 3 days in Venice is perhaps too much.
If you go in Jan, you avoid the summer months, which is nice, as it will be between 30-40C (around 90-100F) with no A/C or good airflow anywhere. It will also be jammed with sweaty tourists. However, in Jan, it will be quite cold (sometimes down to 0F) but you'll avoid the standard tourist rush of the summer. Fall (late Oct early Nov) is really optimal.
Also, I don't find it so inexpensive (1700+airfare seems kind of steep).
Let me propose an alternative:
1. Agrotourismo in Tuscany (you can rent apartment/villa, usually a renovated farmhouse for roughly 200/week with a full kitchen so you can cook what you want ... throw in a car rental for a week and you're still only around 400 with very nice accommodation, better than any hotel, our last "apartment" was 70m2 or about 700 sq ft in the foothills).
Last time I stayed here (in Oct it was 250/week)
http://en.agriturismo.com/holiday-houses/casa-vacanze-scopeto-casole-d-elsa.asp
And to be honest, I didn't find Florence so interesting. You should see it BUT Siena was much nicer (about 50 km south on the FI-SI Autostrada). But, both of those pale in comparison to San Giminagno.
Siena:
http://wikitravel.org/en/Siena (much better feeling and architechture than Florence)
San Gimignano:
http://wikitravel.org/en/San_Gimignano (smaller and in the wine-producing countryside)
You could make an exquisite 11-day trip just around Tuscany alone by car or rail for less money than the package trip. Also, a lot of the Agrotourismo villas are still active vineyards so you can make wine and eat heavenly as well. The food in the cities pales in comparison to someone serving food out of the their house/estate. For example, most of the time we ate without menus, and provided suggestions which were made to order.
If you really want to jam it full, you could even fly into Venice (2 is enough as it's really tiny) and take the train to Florence and (for 3 days -- or more if you're an art history kind of person) and then into the countryside with a car for the remainder and fly back from Florence. You'll see so much more by car than by bus/train and you'll interact with the locals much. much more, which is an experience in itself.
Rome is OK if you're religious, but most of great Italian culture isn't in the cities, it's in the countryside, especially in the small town/villages in Tuscany.
One last thing, Italy is quite cheap once you get away from the tourist areas. Brilliant espresso, better than I've had anywhere else, is 1, for example, but 5 if you're in Rome.
Let me know if you'd like any other suggestions.
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One last thing, bring some extra and stock up on Italian goods.
I highly recommend:
these guys for footwear:
http://www.fiorentini-baker.com/
these guys for bags:
http://campomaggi.it/
these guys for espresso machines:
http://www.lapavoni.it/home.asp?lang=en
I found that the prices for these goods in the countryside were half the price in Germany and about 1/3 of the US price (if 1:1$ when VAT is eliminated). 700 dollar boots (US price) for roughly 200 in Siena.
