When I worked as an employee for someone else, and did something that generated income, the income went to my employer. I got a regular paycheck, not the total profit of the work I'd done to spend as I wished.
Obama works for us (U.S.) Yes he works hard, but he gets a paycheck, and the fringe benefits he earns are off the charts. He won the prize in the course of doing his job.
In this case, I actually agree with George W. Bush.
IT'S OUR MONEY!
The prize money belongs to the United States of America, not to Obama. He should sign it over to the U.S. Treasury.