D&C 26

Shortly after the Church was organinzed, the Lord instructed -

"...all things shall be done by common consent in the church, by much prayer and faith, for all things you shall receive by faith."   (Doctrine and Covenants | Section 26:2)

This new law of common consent has evolved to a more common word of "sustaining" Church leaders and teachers.  Obviously, common consent or sustaining is not to be done at a whim but by "prayer and faith".  Callings were never intended to be by democratic voting or personal preferences or feelings, but by the the authority and keys of the priesthood.  That is where prayer and faith comes in.  President Joseph Fielding Smith taught -

“I have no right to raise my hand in opposition to a man who is appointed to any position in this Church, simply because I may not like him, or because of some personal disagreement or feeling I may have, but only on the grounds that he is guilty of wrong doing, of transgression of the laws of the Church which would disqualify him for the position which he is called to hold.” (Joseph Fielding Smith, Doctrines of Salvation, Vol. 3, p. 124.)

I would suggest that "wrong doing" would be serious transgressions, for all of us have weaknesses and are not perfect.

Another purpose of common consent is that nothing is done in secret but for all that are members of the organization for President Smith continued -

“No man can preside in this Church in any capacity without the consent of the people. The Lord has placed upon us the responsibility of sustaining by vote those who are called to various positions of responsibility. No man, should the people decide to the contrary, could preside over any body of Latterday Saints in this Church, and yet it is not the right of the people to nominate, to choose, for that is the right of the priesthood.” (J. F. Smith, Doctrines of Salvation, 3:123; see also D&C 20:65.)

In that in many cases, what the Lord speaks to one He speaks to all, those called are then instructed that they -

"...shall let your time be devoted to the studying of the scriptures, and to preaching, and to confirming the church...and to performing your labors on the land, such as is required..."  (Doctrine and Covenants | Section 26:1)

I note the obligation of spiritual work as well as temporal work of performing "labors on the land" for support.