The relationship between individual rights and the common good is a fundamental question in political philosophy, and it is certainly an important consideration for the Founding Fathers. The question is really what is more important: the rights of the individual or the good of society. While the interests of an individual do not necessarily run counter to the interests of society, they often do.
From the perspective of an individual, he/she has the power to exercise their rights for themselves. They presumably know how best to exercise them to their advantage, and every individual acting accordingly will make for a free and successful society. Any impingement on that freedom is unacceptable. From the perspective of the common good, however, the matter is not quite so clear. From the perspective of the common good, individuals exercising individual rights does not always result in the good of society as a whole. For this reason, the common good implies that there should be some rights held outside of the control of an individual that are geared to the good of society. Just as it sounds, this means that individuals would have to sacrifice some of their rights (or at least yield) to the larger concerns of a society.
Ultimately, the issue could be perceived as the distinction between a selfish and a selfless attitude toward society. Individual rights focus on the individual, and the common good looks beyond the individual to the community of individuals.