You also need a very, very good antenna for that sort of stunt.
QRP is tough. I'm a licensed HAM radio operator and my Tx has a 5 W final stage, so I fit right into the QRP limits. It's tough. You're at the mercy of the ionosphere all the time.
I use a WSPR transmitter that outputs around 200mW on 20m and am easily heard all over North Americdn and Europe. I've also had two South Pacific reports.
You also need a very, very good antenna for that sort of stunt.
For 10mW, sure, but I've done Michigan to France on 5W with a plain old 40m loop 15-20 feet off the ground. In hindsight, I should have tried it on 3W if only to get 1000mi/W on a cloud warmer.
With the right software, plus favorable ionospheric conditions, you can get really, really good range. This guy did 7,600km, eastern Austria to south Florida: http://gerolfziegenhain.wordpress.com/2013/04/13/raspi-as-ws...