One.

Henry Ford built his first car, the Quadricycle, later in 1896.

But Charles and Frank Duryea did it first.
"On September 20, 1893, in the streets of Springfield, they completed the first successful run of an automobile in the United States." They setup the first American car manufacturing company, and sold 13 cars in 1896.

http://en.wikipedia.org/wiki/Duryea_brothers

So for the entire year of 1894, it seems the Duryea brothers had the only working car in the US.