This is getting silly. This and the other thread. Both focus on the fact that they described slaves as immigrants while completely ignoring the other, more salient, misstatement.
According to Mirriam-Webster (on-line version), an immigrant is
a: a person who comes to a country to take up permanent residence
b: a plant or animal that becomes established in an area where it was previously unknown
Those who made the middle passage were immigrants, by definition.
If, however, you want to pick on Pence (and especially Carson) for general idiocy, then you should focus on the statement that emphasizes they "wanted to build new lives for their families." I have no doubt that this is not what people chained to the decks of Portuguese, Spanish, and Dutch seagoing vessels, being forced to endure rape and beatings, not being able to understand the languages of their captors, having to sleep in their sh
it and urine
en route, and being tossed about by unfamiliar winds and waters, would be thinking about. They'd be thinking about escape, most likely.
Spend your energies wisely. To call them immigrants is not inaccurate; to conclude that African slaves, like most other groups of immigrants, came to the Americas for economic opportunity, suggests willful ignorance.
