The way I see it, if the cities are sprawling (like LA), then cars will rule. If they are compact (like NY), then public transit will at least have a chance.
It's not a matter of if they can build the metro fast enough. If you have a sprawling suburbia, you can't effectively cover enough area to make public transit competitive. (I think this applies to all public transit, not just subways.)
IMO, the secret to effective public transport is having an independent system so you can avoid traffic jams. The reason Bus systems fail is they don't save people time. However, taking the subway tends to be faster than driving when you include parking time etc.
In Minneapolis, light rail to the airport works for this reason, even though it is subject to stopping for traffic downtown. Once past downtown, the train takes precedence, so it really does save time. (Since I have no car in Minneapolis, the light rail makes everything feel like an extension of the Airport/Mall of America.)
Dedicated bus lanes provide a partial solution to this problem, and they tend to be cheaper than subways.
On the other hand, they reduce the speed of traffic outside of the dedicated lanes...Whether that is a bug or a feature depends on whether you are an economist or social planner.
It's not a matter of if they can build the metro fast enough. If you have a sprawling suburbia, you can't effectively cover enough area to make public transit competitive. (I think this applies to all public transit, not just subways.)