The statement from Elon Musk at the car's announcement was 'Has anyone here watched Spaceballs? What's faster than Ludicrous? That's right, Plaid!' So in the Roadster, there is a 'Plaid' mode which enables the 0-60 in 1.8s acceleration, accompanied by suitable graphics on the 17" screen ;)
You'd think that the ability for the wheels to deliver power to the ground has to be the limiting factor at some point.
Most sports cars are at that point at low speeds and either need a skillful foot or an electronic system to prevent burning out. A 1.9 second 0-60 is pretty much the limit on street tires (and requires AWD). Someone will take it even further by putting drag slicks on there.