Does a US citizen need a passport to travel from one European country to another?

I need to travel from Portugal to Italy, but I already used both entries on my dual-entry Portuguese visa. Will I need my passport if I travel round trip from Portugal to Italy?
Include a reference please, thanks.

How long does it take to get a travel visa – American citizen traveling to Mexico?

I’ve never had a travel visa, I’m wondering from the time I walk into the office to the time it is delivered, how long is the process of obtaining one?
Thanks
Yea, I messed up, I meant Passport! Looks like I’ll have to post another question!