While I fully support taxing the crap out of cars, Singapore and the USA are hardly comparable. It's the third most densely populated country on earth, and you can walk the circumference of the entire island in about a day. Not even factoring in the comprehensive public transit..
This can't be stressed enough. Large swaths of the US population would immediately become immobile. I think OP has never lived and worked in a rural area, say 30 miles outside of the nearest town, where survival depends on your ability to transport yourself.
In a way, the invention of the automobile made our lives worse. It meant grocery stores and services could be placed further and further away, stretching out areas rather than condensing them.
Norway and Singapore didn't just switch from large subsidies to large tax. The problem isn't that a country can't function without subsidizing gas. The problem is that people who are used to the status quo will be pissed off when you interfere with their god-given right to cheap gas.