The people of God who are the subject of the prophesies in these psalms are not the elect as you as a Calvinist would define the elect.
"This signifies the set time of love and life to every particular soul at conversion; which is a day for light, and a day of power; when the exceeding greatness of the power of God is put forth in the regeneration of them: and the people that were given to Christ by his Father, in the covenant of grace, and who, while in a state of nature, are rebellious and unwilling, are made willing to be saved by Christ, and him only; to serve him in every religious duty and ordinance; to part with their sins and sinful companions, and with their own righteousness; to suffer the loss of all things for him; to deny themselves, and take up the cross and follow him: and when they become freewill offerings to him, as the word signifies; not only willingly offer up their spiritual sacrifices of prayer and praise, but themselves, souls and bodies, to him; as well as enter volunteers into his service, and cheerfully fight his battles, under him, the Captain of their salvation; being assured of victory, and certain of the crown of life and glory, when they have fought the good fight, and finished their course."
- excerpt from John Gill's Bible commentary on Psalms 110:3
Numberless beauties appear, in this verse, like the constellations of the heavenly borders, to call upon our notice. First, the promise made concerning the people of Christ. Here we find that Christ had a people, a church, a seed, an offspring, before his incarnation: and hence, not only at his birth, but even before his conception, his name was called Jesus, because he should save his people from their sins. Matthew 1:21; Psalms 89:3-4; Isaiah 44:3; Isaiah 59:21. Secondly, God the Father promiseth that this people shall be a willing people; a people of willingness, as it might be rendered; volunteers, listing under Christ's banner. When Jesus is set up as an ensign to the nations, the Gentiles shall seek to it, and his rest shall be glorious, Isaiah 11:10. ... Thirdly, God's promise is, that all these blessings shall take place in the day of Christ's power. The sovereignty of grace, and the influence of his Spirit, which accompanieth his word, shall make it effectual; so that it shall not return void, but like the rain and the snow, which cometh down from heaven, shall give gracious influences; Isaiah 55:10-11. And it is beautiful to remark how variously this day of Christ's power is spoken of in scripture, so as to point out the blessed properties of it: A day of espousals of the soul to Christ, Song of Solomon 3:11. A day of salvation, 2 Corinthians 6:2; hence when Christ made the publican Zaccheus willing in the day of his power, he said, This day is salvation come to this house; Luke 19:9; and a day of the Lord's making and marvellous in our eyes, Psalms 118:24.
- excerpt from Robert Hawker's
The Poor Man's Commentary on Psalms 110:3