What have latter-day prophets taught concerning the prophecy of Joseph Smith that the United States Constitution would hang by a thread and be saved, if saved at all, through the efforts of the Elders of Israel? See Below many quotes from Leaders of the Church. From Josephsmithfoundation.org

Joseph Smith

“Then shall the Lord say go tell all my servants who are the strength of mine house my young men and middle aged &c come to the Land of my vineyard and fight the battle of the Lord Then the Kings & Queens shall come then the rulers of the Earth shall come then shall all saints come yea the Foreign saints shall come to fight for the Land of my vineyard for in this thing shall be their safety and they will have no power to choose but will come as a man fleeth from a sudden destruction But before this the time shall be when these who are now my friends shall become my enemies and shall seek to take my life and shall be m there are those now before me who will more furiously pursue me and the more diligently seek to my life and be more blood thirsty upon my track than ever were the Missouri Mobbers You say among yourselves as did them of old time it is I & is it I But I know these things by the visions of the Almighty.”  19 July 1840, as recorded by Martha Jane Knowlton Coray; ms. in Church Historian’s Office, Salt Lake City; Joseph Smith Papers, LDS Church Historical Archives, Box 1, March 10, 1844 Also: D. Michael Stewart, “I Have a Question,” Ensign, June 1976, 64-65 “Hence we say, that the Constitution of the United States is a glorious standard; it is founded in the wisdom of God. It is a heavenly banner: it is to all those who are privileged with the sweets of its liberty, like the coaching shades and refreshing waters of a great rock in a thirsty and weary land. It is like a great tree under whose branches men from every clime can be shielded from the burning rays of [oppression’s] son.” Joseph Smith, History of the Church, Vol 3, p. 304 (As recorded by Mosiah Hancock) The United States will spend her strength and means warring in foreign lands until other nations will say, “Let us divide up the lands of the United States”, then the people of the U.S. will unite and swear by the blood of their forefathers that the land shall not be divided. Then the country will go to war, and they will fight until one half of the U.S army will give up, and the rest will continue to struggle. They will keep on until they are very ragged and discouraged, and almost ready to give up — when the boys from the mountains will rush forth in time to save the American army from defeat and ruin. And they will say, “Brethren, we are glad you have come; give us men, henceforth, who can talk with God”. Then you will have friends, but you will save the country when its liberty hangs by a hair, as it were. Joseph Smith, as recorded by Mosiah Hancock in his autobiography

What do we know about the purported statement of Joseph Smith that the Constitution would hang by a thread and that the elders would save it?

D. Michael Stewart, Brigham Young University, Department of History The documents show that Joseph Smith did prophesy a number of times that the United States and the Constitution would be imperiled and that the elders would have a hand in saving them. The first known record of the prophecy dates to July 19, 1840, in Nauvoo, when the prophet spoke about the redemption of Zion. Using Doctrine & Covenants 101 as a text, he said, “Even this nation will be on the verge of crumbling to pieces and tumbling to the ground and when the Constitution is on the brink of ruin this people will be the staff upon which the nation shall lean and they shall bear the Constitution away from the very verge of destruction.” (Joseph Smith Papers, LDS Church Historical Archives, Box 1, March 10, 1844.) There are also other documents in Church History files that show that five different early Saints recorded some remarks by the Prophet Joseph Smith on this same prophecy, perhaps voiced by the Prophet a number of times in a number of ways after 1840. Parley P. Pratt wrote in 1841 that the prophet said, “The government is fallen and needs redeeming. It is guilty of Blood and cannot stand as it now is but will come so near desolation as to hang as it were by a single hair!!!!! Then the servants goes [sic] to the nations of the earth, and gathers the strength of the Lord’s house! A mighty army!!!!!! And this is the redemption of Zion when the saints shall have redeemed that government and reinstated it in all its purity and glory!!!!!!!!!!!!!!!!” (George A. Smith Papers, Church Archives, Box 7, Folder 5, January 21, 1841.) James Burgess related that the Prophet, while addressing the Nauvoo Legion several miles east of Nauvoo in May 1843, said that “the time would come when the constitution and government would hang by a brittle thread and would be ready to fall into other hands but this people the latter-day saints will step forth and save it.” (James Burgess Journal, 1818–1904, Church Archives, vol. 1—found among loose sermons.) Orson Hyde recalled that the Prophet predicted that “the time would come that the Constitution and the country would be in danger of an overthrow and said he, if the constitution be saved at all, it will be by the Elders of this Church. I believe this is about the language as nearly as I can recollect it.” (JD, 6:150.) In a Pioneer Day celebration in Ogden in 1871, Eliza R. Snow said, “I heard the prophet say, ‘The time will come when the government of these United States will be so nearly overthrown through its corruption, that the Constitution will hang as it were by a single hair, and the Latter-day Saints—the Elders of Israel—will step forward to its rescue and save it.” (Journal History, MSF 143 #28, July 24, 1871.) Jedediah M. Grant, during the dark days of threatened invasion of Utah by a federal army, referred to the Prophet’s utterance as he addressed a Mormon Battalion gathering in Salt Lake City, February 6, 1855. “What did the Prophet Joseph say? When the Constitution shall be tottering we shall be the people to save it from the hand of the foe.” (Deseret News Weekly, January 19, 1870.) On various occasions, Joseph Smith referred to the Constitution, the country, and destiny of the nation; and there is clear evidence that he anticipated future peril. Furthermore, he pronounced the prophecy at various times and places. Perhaps he himself interchanged the simile “on the brink of ruin,” “hang by a brittle thread,” “hang by a single hair,” etc., to describe the anticipated crisis. It is also clear that the redeemers or rescuers of the Constitution were to be either the Saints generally or priesthood officers specifically. Since no particular time was given for fulfilling this prophecy, members of the Church have often wondered about its timing. The prophecy clearly indicates a single, identifiable episode yet to come. However, it is helpful for us to constantly be on guard against threats to the central elements of the Constitution. It is not wise to sit by and think that the protection of the Constitution is the problem of someone else at some other time. In support of this view of “constant vigilance,” it is most instructive to note that Church leaders have seen the Constitution imperiled a number of times. Brigham Young, reflecting on the prophecy of 1868, expressed: “It would not be many years before these words come to pass.” (JD, 12:204.) President John Taylor in 1884 declared: “It may be nearer … than some of us think.” (JD, 25:350.) President J. Reuben Clark, Jr., warned in 1942: “Whether it [the Constitution] shall live or die is now in the balance.” (Conference Report, October 1942, p. 58.) Students of history and the Constitution know that the Constitution has been imperiled a number of times in its history and has been saved a number of times both by vigorous political action and by vocal public opinion. Thus, rather than simply wait for the one time when the Constitution shall hang by a thread, Latter-day Saints must continually be vigilant. Our commission to save the Constitution is, like salvation, a continuing task, and Church leaders have pointed out the tools available: analysis of constitutional principles, personal study of the history of our nation, reading the Constitution to children at home and in schools, teaching them self-sacrifice—the principle that makes freedom possible—teaching them their obligations as mature citizens, recognizing and resisting ideologies that threaten constitutional principles, and developing loyalty to principle rather than to men or parties. Politicians and statesmen must grapple with tough questions, painstakingly familiarize themselves with vital issues, and be decisive; but finally, an antidote to abusive government, to corruption, and to constitutional peril lies in private character. Humble people in prayerful homes will contribute immeasurably to a lasting constitutional government. And it should be apparent that consistent efforts in these areas will prepare us both to continually protect the Constitution and to prepare us for possibly a yet future rendezvous with our Constitution’s destiny. https://www.churchofjesuschrist.org/study/ensign/1976/06/i-have-a-question/did-joseph-smith-say-that-the-constitution-would-hang-by-a-thread-and-that-the-elders-would-save-it?lang=eng

https://bookofmormonevidence.org/hanging-by-a-thread/