That wasn't a problem for soccer, when most countries didn't have soccer teams but created them for the sole purpose of competing in the Olympics. Furthermore, you could play more than "two games" in the Olympics. Football doesn't have to be played on a Saturday.
I'd said you could only play two games based on the fact it takes virtually every team a week to prepare for the next game in terms of body recovery, gameplanning, etc.
That's not to say, however, it hasn't been attempted. There is such a thing called the International Federation of American Football that hosts a World Cup event and has done so since 1999. They are also trying to get recognition as an Olympic sport.
[ame]http://en.wikipedia.org/wiki/International_Federation_of_American_Football[/ame]
The American team is filled with former college players from across the different divisions within the NCAA, yet, we're not talking the best of competition. Still, we did win the 2007 World Cup by beating Japan in the finals:
[ame]http://en.wikipedia.org/wiki/2007_IFAF_World_Cup[/ame]