So gleerant and riverd0g were discussing for how long Santana's family may have been in the U.S. and whether or not Santana is a first-generation natural-born U.S. citizen (see here).
Glee hasn't given us any definitive answer on the subject yet, but it has given us some context clues, i.e.:
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On "Queso por Dos," Alma Lopez states that her first husband, Hector Lopez, died during the Vietnam War.
In order to have served in the Vietnam War as part of the U.S. Armed Forces, then Hector was likely a U.S. citizen (either naturalized or natural-born), a conscripted nonresident, or, perhaps, a Puerto Rican national with U.S. citizenship.
If the first option, then Alma and Hector could have come to the U.S. from elsewhere no later than 1972, if in fact they did come to the U.S. from elsewhere at all.
Of course, as riverd0g states, they also could have been in the U.S. at a much earlier date, as well, and they may even be or have been natural-born U.S. citizens themselves, depending on Lopez family history.
However.
If the second or third options, then Hector also may not have been a U.S. citizen or a U.S. national at the time he served in the Vietnam War.
It is important to note that we do not yet know for certain what Santana's ethnic background is.
If her maternal family is from Puerto Rico---as Brittany's "little girl in Puerto Rico" line from 6x06 hints that it might be---then it is possible that Hector Lopez could have served in the Vietnam War as a Puerto Rican national with U.S. citizenship conscripted into the U.S. Armed Forces (see here), as an estimated 48,000 Puerto Ricans and persons of Puerto Rican descent served in the U.S. Armed Forces during the Vietnam War.
At this point, we don't know how old Santana's parents are supposed to be, and we also don't know whether Hector or Pedro Lopez is Santana's biological grandfather.
Ivonne Coll (who plays Alma) has stated that Maribel Lopez is Alma's daughter (see here), meaning that Alma is Santana's maternal grandmother, meaning that either Hector or Pedro is Santana's biological maternal grandfather.
If Maribel is the biological child of Hector Lopez, and Hector and Alma Lopez did immigrate to the U.S. from another country, then there is a possibility that Maribel was born outside the U.S.
If Maribel is the biological child of Pedro Lopez, then Maribel was most likely born in the U.S. (as Alma married Pedro after Hector's death).
So TL;DR?
If Maribel were born outside the U.S., then Santana may well be a first generation natural-born U.S. citizen on her mother's side of the family.
However, if Maribel were born in the U.S., then Santana could be a second generation natural-born U.S. citizen or more through her mother's side of the family.
(Thanks to proudlyunicorn and teez-ee for the info on Ivonne Coll!)
(Thanks to Carrie for her thoughts on Puerto Rican nationals with U.S. citizenship!)