According the the Church of Jesus Christ of Latter-day Saints website, it is uncertain that Joseph Smith ever said, “hanging by a thread.” He did say it would be in peril, and that members of the LDS Church would be instrumental in in restoring it, however “hanging by a thread” was commentary from his contemporaries. More modern LDS Church leaders further explained that it will be moral and righteous lovers of liberty from all denominations who would come together to restore the Constitution.
For further explanation on Glenn Beck’s call to action, please visit this article at lds.org, and refer to the last question on the page.