From chapter 5 of the first draft of Selfish Reasons to Have More Kids:

When I was a kid, people often accused others
of “breeding like rabbits.”  If you know
much about rabbits, it’s not a pretty picture: Rabbits get pregnant four times
a year, have litters of half a dozen, nurse their young for only minutes a day,
and boot them out of the nest after a month. 
The point of the rabbit analogy is that we expect more from human beings.  We ought to use our heads to carefully
calculate how many children we can comfortably support, and stop when we reach
that number.  If you don’t use your head,
you will not only be a bad parent and a burden on society.  You will ruin your life.

You don’t hear the rabbit analogy much
anymore.  In part, it sounds faintly
racist.  But the main reason we stopped
comparing people to rabbits is that – at least in developed countries – we
rarely get the chance.  People today have
too much foresight to breed like
rabbits.  Sure, many babies remain the
fruit of impulsive, unprotected sex.  Yet
these babies rarely have a lot of siblings. 
If you look at thirty-something American moms who never married, 45%
have just one child, and 26% have two; married moms in their thirties, in
contrast, are much more likely to have two kids (41%) rather than one (22%).  Almost no one nowadays sticks with a rabbit
strategy after they have one or two unwanted children.

The facts at the end are from the General Social Survey.  If you look carefully at the thirty-something moms, you might notice that compared to married moms, those who never married are equally likely to have 7 kids, and two-and-half times as likely to have eight or more.  However, families with more than six kids are so rare (1% of the married moms and 1.6% of never-married moms) that these ratios mean next to nothing.  Could availability bias plus the extreme behavior of the tail of the distribution account for the popular stereotype of the welfare mom with an army of kids?