JOEL - I can find no scriptures or quotes that specifically mention protection of widows as a duty of the priesthood, but there are some that tell us to take care of their needs. Here is what I could find on the subject:

James 1: 27
27 Pure religion and undefiled before God and the Father is this, To visit the fatherless and widows in their affliction, and to keep himself unspotted from the world.

D&C 83: 6
6 And the storehouse shall be kept by the consecrations of the church; and widows and orphans shall be provided for, as also the poor.

D&C 123: 9
9 Therefore it is an imperative duty that we owe, not only to our own wives and children, but to the widows and fatherless, whose husbands and fathers have been murdered under its iron hand;

James E. Faust said:
"The continuing duty of the priesthood of the Church today is to care for all members, including the poor and the needy, the widows, the orphans, the single mothers and their families. We have an additional duty in our time to increase our labors to love the spiritually poor among our brethren so that they and their families might enjoy “peace in this world, and eternal life in the world to come.” (James E. Faust, “By What Power … Have Ye Done This?” Ensign, Nov. 1998, 45)

Thomas Monson related a relavent story:
"President Clark too was a master teacher. It was my privilege during those years to assist him in the preparation of his manuscripts that they might find their way into printed volumes. What a unique and profitable experience to be with him frequently.
Knowing that I was a new bishop presiding over a difficult ward, he emphasized the need for me to know my people, to understand their circumstances, and, in the spirit of tenderness, to minister to their needs. One day he recounted the example of the Savior as recorded in Luke, chapter seven, verses eleven through fifteen:
“And it came to pass … that he went into a city called Nain; and many of his disciples went with him. …
“When he came nigh to the gate of the city, behold, there was a dead man carried out, the only son of his mother, and she was a widow. …
“And when the Lord saw her, he had compassion on her, and said unto her, Weep not.
“And he came and touched the bier. … And he said, Young man, I say unto thee, Arise.
“And he that was dead sat up, and began to speak. And he delivered him to his mother.” [Luke 7:11–15]
When President Clark closed the Bible, I noticed that he was weeping. In a quiet voice he said, “Tom, be kind to the widows, and look after the poor.” (Thomas S. Monson, “The Bishop—Center Stage in Welfare,” Ensign, Nov. 1980, 89)

"Let the deacons not only assist to keep the meeting houses in repair and their grounds in proper condition, but let them be set to work to look after the welfare of the widows and fatherless, the aged and the poor." (Joseph F. Smith, Apr. Conference. Report., 1908, p. 6.)

"We urge you, particularly priesthood brethren and Relief Society sisters, to be sensitive to the needs of the poor, the sick, and the needy. We have a Christian responsibility to see that the widows and fatherless are assisted. "Pure religion and undefiled before God and the Father is this, to visit the fatherless and widows in their affliction, and to keep himself unspotted from the world" (James 1:27). (Ezra Taft Benson, Conference Report April 1984, Ensign 14 [May 1984]: 7.)

Link to Scripture