No, they won't. Your baby has an amazing immune system — babies come into contact with millions of germs every day and are able to repond to them. When babies are exposed to the small number of antigens in vaccines, the body is easily able to respond to these antigens. Just like contact with antigens in your environment, the antigens in vaccines cannot "use up or damage" your baby's immune system. This is because the body is always making more and more immune system cells, to protect your baby from the millions of germs they contact every day. All vaccines do is ensure the immune system can fend off the most dangerous diseases. It's just like when you give blood, your body quickly makes more. Scientists estimate that an infant's immune system could respond to thousands of antigens, even if they were given at the same time.