I have often heard that murder is unforgivable, that Jesus' atonement does not "cover" it, and that to obtain any measure of pardon (or to reach the Telestial Kingdom), the murderer must pay for his/her own sin in part and even have his/her blood shed. (Blood atonement).
Here is an official statement by the Church in the context of debates about the death penalty, blood atonement, and the extent of the Atonement.
"In the mid-19th century, when rhetorical, emotional oratory was common, some church members and leaders used strong language that included notions of people making restitution for their sins by giving up their own lives.
"However, so-called "blood atonement," by which individuals would be required to shed their own blood to pay for their sins, is not a doctrine of The Church of Jesus Christ of Latter-day Saints. We believe in and teach the infinite and all-encompassing atonement of Jesus Christ, which makes forgiveness of sin and salvation possible for all people."
I realize that one may argue that this statement leaves room for one to argue (1) that murder or David's sin is not covered by Jesus' atonement, and (2) that there is no hope for exalting forgiveness for certain sins, no matter hard one tries nor how penitent or humble one is. For example, the statement is that "forgiveness of sin and salvation" are possible for all people, not that "exaltation" is possible for all people.
As a further example, President Packer made this breathtaking description of the breadth of the Atonement:
"I repeat, save for the exception of the very few who defect to perdition, there is no habit, no addiction, no rebellion, no transgression, no apostasy, no crime exempted from the promise of complete forgiveness. That is the promise of the atonement of Christ." https://www.lds.org/general-conference/1995/10/the-brilliant-morning-of-forgiveness?lang=eng
But in an endnote, President Packer qualified this promise as follows: "Forgiveness will come eventually to all repentant souls who have not committed the unpardonable sin (see Matt. 12:31). Forgiveness does not, however, necessarily assure exaltation, as is the case with David (see D&C 132:38–39; see also Ps. 16:10; Acts 2:25–27; Teachings of the Prophet Joseph Smith, p. 339)."
I am not sure whether by this President Packers meant that it was impossible for David to be exalted because of the nature of his sins, or whether that in the facts and circumstances of David's case, and what he did or did not do subsequently to repent, he would not be exalted.
Of course, I am not in a place to judge David or anyone else, but my hope and faith is the Atonement is truly infinite--that there are no limits on God's power or God's willingness to forgive, save or exalt, that there is always hope, no matter who a person is or what he or she has done. I may be wrong, but that is what I believe.