I suppose it depends on how deterministic one chooses to be. It has been said that Columbus didn't discover America, 3 and 4 masted sailing vessels did. This assumes that once the means exists (and a means that is economically viable among other concerns) given a perceived need it was only a matter of time before someone did it. Similarly the first image was beamed into a florescent screen in an evacuated tube in 1869, so in theory, all the basic components of a TV receiver were available. That it took over 50 years before the first rudimentary TV demonstrations to occur just speaks to the fact that ALL contributing factors must be in place before a tipping point is reached.
Dale Spam pointed out that life as we know it depends on the death of 1st generation stars, somewhat analogous to most mammals depending on the extinction of dinosaurs.
As it applies to human mammals, there is some DNA evidence that seems to reveal that there was either a catastrophic bottleneck or a very long, gradual bottleneck (as much as 100,000 years) when human population hovered around 1000-2000 total individuals. In this state of rather extreme vulnerability, it's safe to assume that some catastrophe, even one beginning with merely an ill-advised tribal decision, let alone some large event like volcanoes or extended drought, could have wiped us out. Likely some other species would have filled the gap then, but "we" as we know it wouldn't be here.
Since the Nuclear Age, and here I do NOT mean nuclear generated power but only explosive weapons (and not to diminish the threat of biological weapons), many scientists including Carl Sagan and Stephen Hawking, have pondered whether our ancient instincts are capable of surviving advancing technology, something like placing a loaded .357 Magnum with a hair trigger in a babies crib.
That said, it seems there is no greater threat than ourselves for some billion years, so if we can rise above that, it's rather impossible to guesstimate how long humankind could continue to exist. There is an upper limit of course which is the ultimate demise of The Universe and who can possibly imagine what we will have learned in 1,000 years, let alone 1,000,000,000 years... and will "we" still be recognizable by "us" today? Yes, it is interesting to ponder.
