The answer to this question is a definite ‘no'. There is no known limit to a child's language learning capacity. It is not the case that the monolingual has one well filled language balloon and the bilingual two half filled language balloons. The child has enough capacity in the brain for learning two or more languages. Some two thirds of people in the world are bilingual and these show that bilingualism and trilingualism are perfectly possible.
It is likely that the bilingual child will not have as large a vocabulary in each language as the monolingual child. Generally, a child's total combined vocabulary in two languages will far exceed the monolingual's in one language. Bilingual children usually have enough vocabulary to express themselves easily and fluently in either language. There may be occasional periods when the bilingual child seems a little behind the monolingual in learning a language. However, this lag is usually temporary. With sufficient exposure and practice, the bilingual child will go through the same language development stages as the monolingual child. Occasionally, the speed of the journey may be slightly slower, but the route through the developmental stages is the same.