We survived a global eruption 70K years ago, leaving us with barely 500 people alive, yet we are still around. Unless something catastrophic happens, like the entire Earth just shatters into a million pieces, we will still be around for a while.
We would already be vanished in 2012,as then the mayan calendar ended. But we are still here.
However, eventually earth will not be there anymore if we humans don't change our way of life. It will not come anytime soon and i don't think i will see it, but i can be that the new generation which are born now will have a tough time already.
If it continue at this speed, then it could be somewhere in 22th century or the 23th century it's end of the story.