It is most likely that at this point it time there was not a widely circulated copy of the plates of Nephi - neither the large plates, nor especially the small plates on which these statements are being written. Therefore, when Jacob references the "promises which we have obtained" he refers to a common knowledge rather than a specific text. Nevertheless, we have many texts in Nephi's small plates that discuss these promises. For the purposes of Jacob's text, perhaps the most important is Lehi's statement:
2 Ne. 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.
Lehi notes that this is a land of promise, but that the promise contains conditions. Prosperity will follow righteousness. The unstated contrary position, however, is precisely the point that Jacob speaks to. In addition to the promises, Nephi's people also surely know of Nephi's vision of the future of their children which occupies our 1 Nephi 12-14. Thus they have promises and prophecies. Jacob reminds them of the promise, but is concerned with the prophecy.