I think, even with friends putting you up for free in Rome, I would budget $250US per day for a 10 day trip to Italy for 2 people. That gives you plenty extra for a splurge meal a couple of times, entrance to museums, a daytrip from Rome to Pompeii, some budget wiggle room for a room in Venice.

Oh - and with 10 days, keep it to Rome, Venice & Florence.