Um not to be argumentative, but your math is contradictory. (actual values are circumspect, but using the numbers you provided, doesn't the math work this way?)
6 billion people population (multiplied by)
1% death rate per year (divided by)
365 days per year = 164 K deaths per day
6,000,000,000 X 1% = 60,000,000 / 365 = 164,383.xx
Extinction would be a concern if there were no births or the birth rate was significantly less than the death rate. We are however a very reproductive species.
21 births per year per 1000 people = 126,000,000 births per year = 345,205.xx births per day*
We are being born at a rate of a little over 2 births to 1 death.
*http://ieet.org/index.php/IEET/print/166/ statistic as of 2005