If you want to claim them as a dependent. They CAN NOT make you get your child a social security number
http://www.ssa.gov/pubs/EN-05-10023.pdf
Must my child have a
Social Security number?
No. Getting a Social Security number
for your newborn is voluntary. But, it
is a good idea to get a number when
your child is born. You can apply for a
Social Security number for your baby
when you apply for your baby’s birth
perhaps they cannot make you at birth however, you can't take the deduction without one.
therefore you will have to apply at some point between birth and filing of birth year.