This is pretty much exactly what soccer goes through in Australia (and JohnT's response is pretty much that of a large number of Australians too!)
Here soccer has three other codes of football to compete with (Rugby Union, Rugby League and Aussie Rules) as well as cricket. It's increasing in popularity at club level, pretty close to rugby league but well short of the AFL.
At an international level the Socceroos are now arguably the most-followed national team, eclipsing the Wallabies (rugby union) ... everyone watches cricket but our national team is in a bit of a lull, and it's more of a pastime than a sport anyway...
Like in the USA, despite being around for a long long time It has also largely been seen as an 'ethnic' sport played mostly by immigrants but this is changing.
It has always had massive participation but the other footy codes have in the past tended to snap up the most athletic kids (the AFL will sometimes draft kids that are stars at basketball and stuff but have never kicked a footy) - I think this is changing now that there are better professional pathways and the game is far more 'mainstream'.
Also like the USA, Australians are used to dominating in international sports so it can be a tough sell getting people interested in a global game where we're not really expected to do well against the top teams...
And things are changing, we're getting gradually better but it will be a long slow road to get anywhere near the top of the pile