Kurzweil's point is the following: "who cares". Even if it takes one-thousand years, it's a blink in the history of humanity / life.
I certainly hope this prediction is true. But I think it has more to do with that fact that Kurzweil will be creeping towards the end of his life (gauged by average U.S. life expectancy) in the next 15 years.
The obligatory note: the true immortality is unattainable in principle without indestructibility (which is something that is hard to imagine even theoretically). Otherwise people will continue to die, en masse, from various unnatural causes. My guess as to the half-life of a human in the best of circumstances is just a couple of hundred years...