TechNo,
I suspect that you probably saw a UFO the other day (or more likely a satellite or the ISS) rather than one of the NEOs.
If the quoted magnitudes are correct on your link, there is no way any of these could be seen with the naked eye, or even with huge amateur telescopes.
Sky magnitudes are quoted on a reverse logarithmic scale, so the bigger the number, the fainter the star. Really bright things have negative numbers.
As an example, the sun has a magnitude of around -27 whilst the full moon has a magnitude of about -13. Although this doesn't seem very different, because it's a log scale it shows that the sun is about 400,000 times brighter than the full moon.
The brightest star (Sirius) has a magnitude of about -1.5 and the maximum brightness of Saturn is around -0.5.
The faintest stars visible with the naked eye in an urban environment are around +3 to +4 magnitude and "down" to around +6.5 magnitude in excellent viewing conditions (you should be able to see around 10,000 stars in these conditions)
Uranus has a magnitude of around +5, although this tends to depend on how hot the curry was you ate on the previous night.
With a decent pair of binoculars, you can resolve down to magnitude +10, and with a 24" telescope (that's 24 inches wide !!) with a 30 minute exposure you could see magnitude 22 stars.
So, with magnitudes well into the 20s, it's unlikely that we'll ever see any NEOs with our naked eyes or even with half decent telescopes until they get VERY close, ie. in the earths atmosphere.
Still, it's still interesting to realise how busy our local space actually is.