My flight will arrive Newark at 19:49 Terminal C and my connectiong internation flight will start at 20:35 Terminal C. There is no change in terminal, I just have to change the plane. Is this enough to manage? I am worried because layover is just 45 mins.
The "Minimum Connection Time" for United Airlines for connecting from a domestic flight to an international flight at Newark is 40 minutes. So technically, this is a "legal" connection.
However given that international flights generally start boarding 50 minutes before departure, and finish boarding 15 minutes before, it's also clearly a very tight connection - 30 minutes from your flight landing to (technically) the door closing on your outbound flight.
If your inbound flight is on time, then there's a good chance you'll make it. Newark terminal C isn't small, but it's not all that large either - and there are carts that you can potentially flag down and get you to your gate faster if you are cutting it very close.
However if your inbound flight is at all delayed - which isn't uncommon for EWR - then you'll almost certainly miss your connection. The problem with missing an international connection is that frequently there isn't another flight to the same destination for (at best) many, many hours, or potentially the 24 hours later. Presuming both flights are booked on the same ticket then the airline will look after rebooking you onto a later flight. If the delay was caused by something in their control they may even give you a hotel voucher if you need to stay overnight - but there's certainly no guarantee of that!
Personally, I would never risk a 45 minute connection at Newark when connecting to an international flight. It's far less about the chances you'll make it, and far more about how long you'll need to wait for the next flight to wherever you're going.