Found Some Rooms
Splendide Royal at $672.29 per night, plus tax
Bettoja Massimo D Azeglio at $332.26 per night, plus tax
Forum Hotel at $362.00 per night, plus tax
Borromeo Hotel at $206.86 per night, plus tax
Another idea is to just stay in a nearby city, like Florence, and take the train to Rome. NOTE: Buy your train tickets NOW, even if you haven't left for Italy yet! Can you imagine the lines at the train station? Mama mia! Trenitalia has updated their list of added trains to/from Rome.
Also check Reid Bramblett's site (Reid is an editor for Budget Travel, an Italophile and author of numerous guidebooks) for some creative ideas on lodging, such as camping, European motel chains, convents, etc.