NASA has been tasked with finding 90% of all the potential asteroids of 140 meters or larger with a chance of impacting Earth in near future - and they have been asked to complete this survey by 2020. Which is possible using new giant telescopes planned to be finished before then.
SpaceGuard has already found over 90% of all the potential asteroids of 1 km or more.
It depends on the size of asteroid. If it is a small one, 50 meters or so - just large enough to get through the atmosphere to the ground level - and do a fair bit of damage - might well have no warning at all - or only a few hours of warning even by 2020. As we saw with that meteorite over Russia a while back.
If you are concerned though about big ones like the one that brought an end to the Dinosaurs - say 10 km in size - well the chance that there is anything that large headed our way before 2100 is well under 0.0001%.
In other words - there are more productive things to be concerned about.
It will happen eventually, that's for sure - unless we divert them - even quite soon compared with geological timescales - but the chances are that it is far enough into the future so that we have evolved to a new species by then, perhaps a hundred thousand generations into the future or more.
As for ones large enough to make humans extinct, even with all our technology - just forget about it. That's not likely to happen even in the next few hundred million years. Chances are the seas will boil dry first.
But - for ones small enough to cause a tsunami - or to destroy a city - and - at a rather lower level - those are the ones that the SpaceGuard program is focused on. There is a chance they might happen before the end of the century - just a few percent - not a huge chance - but might happen.
There's also a tiny but significant chance of larger ones more global in their effects say 1-2 km or so, before 2100, maybe 0.01% or so.
By 2020 we should have found almost all of those ones - and either found one headed our way and be looking for a way to divert it - or else - found that the chance that any exist is tiny.
Can't totally rule it out. Are for instance comets coming in for the first time from the Oort cloud. But those also - if large - then we'd spot them at least some months in advance. And as for very large comets from the Oort cloud - well they are included in the same calculation as all the other large impactors as that is estimated by looking at the cratering record which lumps together comets with other large impactors.
BTW there is a privately funded foundation working on this also, the B612 foundation. Sentinel Mission
Which aims to send a space telescope to an orbit close to Venus so looking outwards towards Earth and would map 90% of all the NEOs of 140 meters or larger by 2020 (which is also a NASA objective)