This is a president who fundamentally believes that the next century is the post-American century. Perhaps it will be the Chinese century. He is wrong.
A few things. What makes him think Obama thinks that? Where did he say that or what action demonstrates that belief? Notice the second sentence. That strongly suggests he just pulled that first sentence out of his ass. If Obama actually said something or did something he wouldn't say "perhaps" and then suggest a country. But Romney and pretty much every Republican since Obama was elected knows they can say what they want while rarely being called on their lies.
This is in big part because the press doesn't hold them accountable enough. Reporters should be asking the questions I just asked in the paragraph above. And if he doesn't have either a quote or can explain an action by Obama they should call it what it is, a lie. But too often the press just lets them say this crap and doesn't forcefully explain what the truth is. They just present two arguments and don't make clear what the truth is. If Romney and others were loudly and consistently called liars when they lie you would think they would stop doing it.
The other thing is something Matt Yglesias said, which is that how can Romney be so sure the next century will be one where the US continues to dominate? Again, Romney has no idea. This is that firmly held thought on the right that the US is the greatest thing ever and just because they think that it will continue to be true no matter how much they screw things up. Like most things with Republicans, its pure tribalism. Its all about how great they are and anything that is different than them is bad. That's why they can so flippantly lie about things. And the only way to combat that is to just as ferociously call them on it.