"Current studies do not support the hypothesis that multiple vaccines overwhelm, weaken, or “use up” the immune system. On the contrary, young infants have an enormous capacity to respond to multiple vaccines, as well as to the many other challenges present in the environment. By providing protection against a number of bacterial and viral pathogens, vaccines prevent the “weakening” of the immune system and consequent secondary bacterial infections occasionally caused by natural infection."

"The neonate is capable of mounting a protective immune response to vaccines within hours of birth. For example, neonates born to mothers with hepatitis B virus infection mount an excellent protective immune response to hepatitis B vaccine given at birth, even without additional use of hepatitis B virusspecific immunoglobulin. In addition, BCG vaccine given at birth induces circulating T-cells that protect against bacteremia and subsequent development of miliary tuberculosis and tuberculous meningitis."

"Although we now give children more vaccines, the actual number of antigens they receive has declined. Whereas previously 1 vaccine, smallpox, contained about 200 proteins, now the 11 routinely recommended vaccines contain fewer than 130 proteins in total. Two factors account for this decline: first, the worldwide eradication of smallpox obviated the need for that vaccine, and second, advances in protein chemistry have resulted in vaccines containing fewer antigens (eg, replacement of whole-cell with acellular pertussis vaccine)."

"Vaccinated children are not at greater risk of subsequent infections with other pathogens than unvaccinated children. On the contrary, in Germany, a study of 496 vaccinated and unvaccinated children found that children who received immunizations against diphtheria, pertussis, tetanus, Hib, and polio within the first 3 months of life had fewer infections with vaccine-related and -unrelated pathogens than the nonvaccinated group."
http://www2.aap.org/immunization/families/overwhelm.pdf