From a software point of view, nothing should happen. When I worked for SONY Psygnosis (developers of the WipEout series) we did something called a 'Soak test'.
Basically you leave a game running for at least 24 hours. You also do it paused. This is to make sure that the game is robust enough. They still do these tests now for PS2 games - so therefore PS2 hardware must be able to handle it.
BUT...
I simply would not recommend leaving a PS2 on that long, just in case you do damage it. Besides not understanding why you would leave a game paused for 2 days, I wouldn't like to take the risk.
My advice? Don't do it man!
- S