I agree that at some point (probably reasonably early on actually) it would start taking longer to say the number out loud than one second, so you'd fall behind.

However we're talking about counting which is not necessarily saying it out loud. You could just be pushing a button every second, or watching a drop of water fall from a pipe at a constant rate.

Anyway, I remember learning this little fact as a kid and it making the numbers (and the difference in magnitude between them) much more tangible.

For context, at a rate of 1/sec/sec:

  1             = 1 sec
  10            = 10 sec
  100           = ~1.5 min
  1000          = ~17 min
  10,000        = ~3 hours
  100,000       = ~1 day
  1,000,000     = ~12 days
  10,000,000    = ~4 months
  100,000,000   = ~3 years
  1,000,000,000 = ~32 years

It may also be worth noting (when discussing national debt and the like) that 1 trillion = ~32,000 years.