As per Alan Taylor's American Colonies, the economy in the south was eventually, but not immediately, completely dependent on slavery. The northern economy less so.

When the New England area was successfully colonised, the landscape (lots of hills and dense forest, cold winters) didn't really lend its self to massive farms and so communities started out with basic subsistence farming, families supporting themselves essentially.

Whereas in the southern colonies, much flatter and open land with a temperate climate lent itself directly to mass farming operations on varying crops down the years. Huge farms mean you need a work force to work the land, unlike in New England where families were essentially getting their sons to help with the family crop.

In the beginning, mass immigration from European countries (especially England) is where the workforce came from. This came from various groups of often single men. Some of these were indentured servants - i.e. they were desperate to get away from a difficult life at home and try for an opportunity at a better life. Problem is these men were too poor to be able to afford the Atlantic crossing so they would agree to pay their way by working for X number of years on a farm on arrival before being awarded their freedom.

And so for a great many years, legions of white Europeans were shipped in to prop up the farms in the southern American colonies, i.e. Carolina, Virginia, Georgia etc. But this model was unsustainable. A huge proportion of the workforce would be dead within a couple of years, usually from disease, and the rest eventually earned their freedom. Also, with the lack of women, the population itself wasn't sustainable, but those that did marry and reproduce, well their families were not required to work for the landowners, they were born free. So you can see the problems landowners had here - their workforce disappearing year on year, and having to constantly replenish from those coming over on ships from Europe.

And so came the slave trade. It eventually became much more profitable for land owners to purchase slaves. Although slaves were expensive, and although they would also die in large numbers due to disease, they did not earn their freedom. Ever. Not only that, the children of slaves would also, automatically become the property of the land owner. This meant generations of men and women could be and would be born into servitude. Suddenly, its much more economically savvy for the landowners to buy slaves, even though there is quite a substantial outlay in the beginning. This economic change was only made possible because of timing really. It just so happened that elsewhere Europeans were successfully stealing humans from Africa (in brutal fashion), and they found a market for those humans in the American colonies.

So yes it is true that slavery made a massive contribution to early American economic growth. It was the bedrock of the southern economies for generations.

New England was not totally innocent of slavery, but it was certainly on a lesser scale than the farming colonies in the south. As the decades passed, New England's economy was very much based on trade rather than farming, and trade didn't require quite so many hands in labour.

It may be an interesting discussion point - partially related - that Taylor's narrative brings the realisation that racism was born from slavery rather than the other way round. I've already suggested that the fact slaves were black was merely an accident of timing - they just happened to be coming in abundance from Africa, but racism wasn't necessarily rife in the American colonies initially. Indeed there are early accounts of black land owners and even black slave owners (though these were certainly fewer). However, the white land owners were quickly presented with a problem, they were few, and their workforce was many. Not only that, but they spoke their own languages and had their own cultures and of course would have had a desire for freedom. Naturally the slaves were likely to band together and make bids for freedom (this did happen a lot, and successfully in many cases). So the white landowners, ostensibly out of paranoia, came to regard their workforce as a threat. They hand to mitigate against this threat with the only method they could see available to them - brutal subjugation. This in turn would change the risk they faced. They were now afraid, not just of "jailbreak", but overthow. In many cases the slaves were not allowed to congregate in large numbers, so as to stop them from creating too much unity between them (which is to risk an uprising).

You can see how "us and them" mentalities would quickly brew, and in only a couple of generations, racism was completely entrenched, as a direct result of slavery, and the effort to subdue the workforce.

Sorry I veered off topic for longer than I intended then.

EDIT: I just want to add, that not all slaves were stolen from Africa as I say above. They were also purchased in great numbers from African magnates who ran their own brutal regimes.