It seems unlikely that Jacob was referring to widely circulated copies of either the large plates of Nephi or (especially) the small plates. Therefore, the “promises which we have obtained” are probably common knowledge developed through public sermons like his own. Jacob does not elaborate on the promises, but they are based on the vision of the future of the Nephites in relation to the Nephite foundational promise that Lehi gave in 2 Nephi 1:9:
Wherefore, I, Lehi, have obtained a promise, that inasmuch as those whom the Lord God shall bring out of the land of Jerusalem shall keep his commandments, they shall prosper upon the face of this land; and they shall be kept from all other nations, that they may possess this land unto themselves. And if it so be that they shall keep his commandments they shall be blessed upon the face of this land, and there shall be none to molest them, nor to take away the land of their inheritance; and they shall dwell safely forever.
As Lehi notes, the promised prosperity is conditional on the people’s righteousness. Jacob, however, is addressing the unstated contrary—that misery and captivity will follow unrighteousness. In addition to this promise, Nephi’s people also surely know his distressing vision about their descendants. (See commentary accompanying 1 Nephi 12–14.) Thus, Nephite culture is schooled in both promises and prophecies of their future. Jacob reminds them of the promise but focuses on the prophecy. The Nephites’ foundational promise is always both a blessing and a curse, depending on their righteousness.