What is the horizontal distance needed to observe an object just as badly as if it where in space at the zenith?
If the atmosphere could be redistributed so that it has sea level density $D$ up to height $H$ and $0$  density above that, then we can calculate 
$$H = \frac{P}{gD} = \frac{100,000}{9.8 \times 1.27} \approxeq 8,000$$
(SI units), where $P$ is sea level pressure.

So it is the same as looking through $8$ km of air horizontally.