No, there were never any white slaves in (what would become) the United States. Europeans had a powerful cultural prohibition against the enslavement of other Christians, and "slavery" as we think of it today was only possible once non-christian, racially distinct groups of people became available for sale.

Your sources are likely confusing an institution known as indentured servitude with slavery; under this system, Europeans were brought to the colonies free of charge, and in return signed on to labor for someone else for a set period of time. This was a coercive labor system, in that once someone agree to an indenture contract they could not back out, and the "masters" of these "servants" had considerable power over them - but the servants were bound by contract rather than for life, and they retained most of the other rights and privileges of legal persons. "Slavery" in this context means something quite different; slaves were treated as property, rather than persons, they were slaves for life, and there were basically no limits on masters' power over them.

I've seen lots of people argue that indenture was sometimes like slavery in that it was obviously an exploitive and harsh system of providing and controlling labor - and there's certainly some truth to that. But there many very important differences between indenture and slavery in the Americas, so it's very important to use the proper term when you talk about these things. Describing indentured servants as "slaves," in other words, risks conflating two completely different things. You won't find any respected/reputable historians who are willing to refer to the "servants" of the seventeenth and eighteenth centuries as "slaves," because the experiences and legal status of indentured servants was fundamentally different from and can't really be compared to that of slaves.

How are you defining "slave"?