The Earth's spin does not counteract gravity itself along the equator. Rather, it causes an outward centrifugal force that counteracts a portion of the inward gravitational force. However, this effect is very small compared to the overall gravitational force holding everything to the Earth's surface. 

You can actually prove that mathematically:

Assuming the Earth is a perfect sphere, the surface of the earth would have to spin at the orbital velocity for an object at the surface of the Earth. Using the circular motion equation: a=v^2/r,

9.8 = v^2/6,371, 000

V= 7900m/s, 7.9km/s or 4.91miles/second or 17,700mph

The Earth would need to rotate about once every hour and a half, or about 16 times faster than it currently does.

This is similar to the speed of the international space station. 4.76miles/second or 17,150mph because it is in low Earth orbit.
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