FCO to AMS

Rome to Amsterdam is within the Schengen area and essentially an internal flight. You won't have passport control or customs, only the regular check-in and security.
Three hours is over the top. Be at the airport two hours before departure and you'll have enough time left for a last real Italian coffee.

I agree 2 hours is good for that flight. You are probably flying KLM so would depart from Terminal 1 and not have need for customs related concerns since you are flying within the Schengen area.

Only saying even 2 hours because FCO is such a large airport and therefore subject to longer possible delays.
The flight is the equivalent of flying from say Chicago to New York City.

So since this is basically an internal flight within the Schengen Zone would there then be any extra measures flying from Amsterdam to Atlanta other than a passport check since nothing further was done in Rome? I'll be flying KLM the whole time.

When we flew FCO-AMS-ATL, there was extra security before the ATL leg of the journey, including passport control and even the need for any liquids over 3oz to either be discarded or in one of the "duty free" sealed bags that could not be opened. You will then go through customs when you arrive in ATL.

Piggybacking on this thread...
So how long would one need at AMS if coming in on a budget airline and leaving on a US carrier?

Yes there are extra security measures before flying to the US. There will be passport control, since you are leaving Schengen, and you will have an extra security check to go through.
If you fly KLM all legs, a layover of 90 min is sufficient. Those who travel with different airlines and need to check in luggage again, need much longer than that.

My first flight from Rome to Amsterdam is KLM and my flight from Amsterdam to the U.S. is Delta. Would I still have to get my bags and recheck them in Amsterdam even though KLM and Delta are close partner airlines?

"My first flight from Rome to Amsterdam is KLM and my flight from Amsterdam to the U.S. is Delta. Would I still have to get my bags and recheck them in Amsterdam even though KLM and Delta are close partner airlines? "

It depends.

If you are all one one ticket, your bags should be checked through to the US. Make sure when you check in in Rome that your bags have the tag for your home airport. You then should not see them until your first US airport. Regardless of your final destination, at your first US airport you go through immigration (passport control), then retrieve all checked bags, then go through customs. If your first US airport is your final US airport, you just leave the airport and go home. If you are connecting to another flight, just outside the customs door, there is a Baggage Recheck area; you deposit your checked bags there, then go to your next flight (going through security on the way, since you have now left the secure area).

If you are on separate tickets, KLM may or may not agree to tag your bags to your final destination, or may insist on tagging them only to Amsterdam. Ask, and double check yourself; if the tags say AMS, you have to retrieve them in Amsterdam and recheck them to the US.

Once upon a time, airlines routinely agreed to tag bags across tickets and airlines; now, it's common for them to refuse, but they can also agree. As I said, though, if you are on one ticket, don't worry - your bags will definitely be checked through to the US (although it never hurts to double check the tags yourself - know the airport initials).