Her annotation of part of psalm 18 says it all:
He rewarded me because I was just, (When have I been just?)
repaid me, for my hands were clean, (My hands are filthy!)
for I have kept the way of the Lord (No, I haven't)
and have not fallen away from my God. (Yes, I have)
It's true. In praying these lines it is hard to own them. They seem to accuse the pray-er who knows that they aren't true. Rather than the bold proclamation of the psalmist, they seem to enforce upon the pray-er her sense of inadequacy and distance from God and his righteousness.
This experience demands a theological account of Christian prayer. What do Christians mean by prayer? Christian prayer is first and most completely the prayer of Christ. As Sancrosanctum concilium 83 puts it, "Christ Jesus, the high priest of the new and eternal Covenant, took our human nature and introduced into the world of our exile that hymn of praise which is sung in the heavenly places [in supernis sedibus] throughout all ages.
So, by Christian prayer we mean first and foremost the prayer of Christ. We who are Christians, then, have as our praying project to simply join ourselves to this prayer. Note the General Instruction of the Liturgy of the Hours 6: "Prayer directed to God must be linked [conectatur oportet] with Christ, the Lord of all, the one mediator through whom alone we have access to God." This is why Christians always pray, 'through Christ our Lord;' our prayer is meant to be taken up into his.
In the end it is not us who pray at all, but the Spirit who prays within us. Thus prayer is the real fruit of our being baptized into the life of the Blessed Trinity. Just as the Spirit conceived the Word of God that He might borrow our humanity from Our Lady, so the Spirit delights to conceive the prayer of Christ in the lives of those who consent to be Christians.
So when we come to praying the psalms, for instance, the primary praying voice is not ours, but Christ's. He is the righteous one who can pray "my hands are clean' and 'I have kept the way of the Lord.' Christ can pray this prayer even thought we can't. But since Christian prayer is the prayer of Christ, the righteousness that we hold up to God in sacrifice through our prayer is not our own but Christ's. It is by his righteousness and obedience that we are saved, after all, not by our own. When we pray these lines it is His voice praying, and his perfect and eternal sacrifice in which the Father delights.
On the level of day to day spirituality, then, Christian prayer is not matter of effort but of consent. The prayer is always there, as the Holy Spirit has stretched the perfect praise of the Blessed Trinity to include our humanity in the Incarnation. We just have to permit the Spirit to pray within us, through Christ our Lord, that his prayer might take shape in our humanity as well.