In answering this question, we must first be very careful to avoid assigning causality to the parallel developments of slavery and liberty. That is, we must be careful not to assume that the advance of slavery caused the colonists’ sense of liberty to grow or vice versa. I would argue that these developments were largely parallel and not really connected to one another.
Over the course of the 18th century, the colonists’ sense that they should have liberty grew. This was due, in large part, to the fact that the British government left the colonists alone for much of this century. The British, preoccupied with other matters, practiced a policy of “salutary neglect” with regard to the colonies. The colonists came to regard this as the natural state of things. As this policy continued, colonists came to feel that they had a right to the liberty that they had been granted by accident.
At the same time, the system of slavery was growing and becoming more entrenched. This was due mostly, however, to economic pressures. It was clear that the Southern colonies’ economies were going to continue to rely on growing staple crops for export. It was also clear that slavery was going to be necessary in order to keep that economy going. At the same time, much of the Northern economy was supported by the Atlantic slave trade and by the Southern plantation owners’ need for goods and services. Therefore, slavery continued to become a bigger and bigger part of the American economy and society.
Eventually, these trends intersected. The slave system became as important to America economically as the idea of liberty was in political terms. In a way, it is possible to say that the growth of slavery helped to push the idea of liberty. We can argue that the presence of slavery gave the American colonists an example of what they ought to fear. Because they saw how badly they were treating their own slaves, they came to worry even more about being “enslaved” in any way themselves. In this way, at least, we can say that the two came to be connected in a small way.
Thus, I would argue that the idea of liberty on the one hand, and the slave system on the other, grew in parallel for much of the 1700s. The two were not necessarily connected in any causal way. However, both became very important to American colonists by the time of the Revolution and both were integral aspects of our society at that time.