I am flying from the US to Warsaw. I go thru Copenhagen and they only allow 45 min from one flight to the next can I make it. I will have 1 checked bag and a backpack.
As Copenhagen and Warsaw are both in the Schengen area, you will immigration in Copenhagen. Although you won't need to get you checked bags, immigration could still take a while, depending on when you arrive.
If you booked both on the same ticket, your carrier has a responsibility to get you to Warsaw, so even if you miss your second flight (e.g. if your first flight is delayed), you should be on the next flight.
If you booked the tickets separately, then it's your responsibility to get to Copenhagen on time for your flight to Warsaw, and a late flight from the US is not a valid excuse. You would be responsible for any fees from changing the time of the flight.
It all depends on your airline. I was in a similar situation this year, flying back from London to Tokyo via Hong Kong. There should have been a 2 hour transfer time but due to a late start and bad weather, we arrived with only 45 minutes until the next flight.
I was flying Cathay Pacific and they really impressed me, as soon as we got off the flight there were attendants waiting with signs for the different connecting flights. I joined the group for Narita, Tokyo and we were taken through a special immigration check route which bypassed the queues. I can only imagine this is normally reserved for first class passengers.
All told I was in Hong Kong airport for just 15 minutes before I boarded my next flight. Without a doubt, the shortest transfer time I think is possible in an airport that size.
If you're flying with two different airlines I don't think you'll make it in 45 minutes.