In this case we have an actual named asteroid for 24th September it is easy to look up its Closest approach table. Notice that it misses by 0.0625 AU. If you aren't used to astronomical units, that may seem a close miss. But that's a distance of 9.35 million kilometers. The Moon is only 0.3844 million kilometers away. So that's a big miss there. And the minimum distance is 8.33 million kilometers. It's going to miss by more than 21 times the distance to the Moon. So no need to be concerned about that one!
Anyway so in summary, just visit this page, automatically updated for the Sentinel program: Current Impact Risks. Just look and see if there are any entries coloured orange or red. Then look for the predicted date of impact. So far this has never happened.
Searching for asteroids in the first place is an international thing, many countries participate - and it's based on wide field of view telescopes.
It would be totally absurd to e.g. dedicate Hubble to search for asteroids, when a wide field camera can do, several times a minute, what would take Hubble probably hours to do with its tiny field of view. Tying up one of the most expensive telescopes in the world to do something it's not designed to do, when we already have many far better telescopes for the job world wide, running every night, full time, looking for asteroids. And even if it did, the other telescopes would beat it hands down in terms of numbers of discoveries.
And then you can't tell where exactly an asteroid is going from just one observation or even a week's worth of observations. So you'll have no idea if it is on an impact course. Being at NASA again will help nothing there, what you need are more observations. And again, it would be absurd to use the world's largest telescopes for that (except in some very special situations).
So, for that, we depend on many amateur and international astronomers observing to keep track of them and refine the orbits.
It's really one of the sillier of the conspiracy theories, when you have a bit of background...
This sort of thing distracts people away from the things that are real issues in the world that they should be concerned about.
But this is a petition to increase spending on asteroid defence 100 times. On the basis that unusually amongst the many natural hazards we face - this is a hazard we can do something about with our technology
- already signed by many famous astronomers and astronauts.
OR SUPPORT SPACE TELESCOPE TO LOOK FOR THEM
You can also donate to the B612 foundation who aim to put a dedicated asteroid watching telescope into orbit.