Don't know much about Italy in particular, but generally in Europe the duties of a nurse can be quite different from those in the US. The big problem, however, is having your Stateside nursing credentials recognized in the EU. The individual countries are allowed to require that you speak, read and understand the local language fairly well and most countries require even other EU nationals to take some re-training classes geared toward how the national health care system works.
I agree with Bev. Italy is notorious for putting real or artificial barriers on foreigners wishing to practise their profession. Even EU nationals, who under EU law should enjoy mutual recognition of qualifications, have to jump through hoops to get their qualification verified, register with professional body and finally be allowed to practise. I have heard of a physiotherapist, qualified in UK, taking over a year to get her qualification recognised in Italy. There is usually a rule of a sort, but just meeting it doesn't guarantee success. The regulator can and do ask for additional papers (all officially translated into Italian of course). Then nothing happens for 6 months. Then they ask for another paper. Then nothing. And so on. It's so frustrating not knowing what's going on, but you just have to wait, as you as an applicant has no rights and can't do anything to hurry the process. For non-EU qualification. I'd imagine it will be even more complicated.
Contact the American Hospital in Rome for their interpretation of how US qualification is recognised. Also you will probably need work permit and visa, and the ease of getting one depends on whether nursing is classed as a shortage occupation.