The Psalm reading for tonight's Liturgy of the Lord's Supper is one of my favorites, Psalm 116, which is a Todah psalm and part of the "Hallel" (Praise) Psalms (Psalms 113-118) that were and are traditionally sung during the Passover meal.
I've reading slightly different opinions among scholars about how exactly the Hallel psalms were incorporated into the ancient Seder celebration. According to one view, Psalms 113-114 were sung early in the rite, and Psalms 115-118 after the drinking of the third cup, the "Cup of Blessing."
It is striking and moving to re-read Psalms 115-118 and ponder the fact that Jesus of Nazareth sang these Psalms with his disciples just before going out to what he knew was his certain death.
That Jesus knew of his imminent death (and resurrection) is particularly strongly attested (ironically) in Mark, regarded in critical scholarship as the earliest and most historical of the Gospels (Mark 8:31, 9:31; 10:34).
If you re-read Psalms 115-118 today, you may be powerfully struck by how thoroughly imbued they are with the theme of salvation from death:
Ps 116:8: "You have delivered my soul from death ..."
Ps 118:17: "I shall not die, but live, and recount the deeds of the Lord ..."
Keep in mind that Psalms 116 and 118 are Todah psalms, psalms written to accompany the Todah or "Thanksgiving" sacrifice in the Jerusalem Temple. This is explicit in Psalm 116:17. Todah in Greek is "eucharistia."
The Messianic reading of the Psalms--that is, understanding the Psalms to be speaking of the Messiah--is not at all a Christian innovation. The end of the Qumran Psalms scroll (11QPsalmsA) says, "David spoke all these by the Spirit of prophecy ..." In Matt 22:41-46, Jesus does not need to convince the Pharisees that Psalm 110 is to be understood of the Messiah--they took that for granted. That the Psalms speak of the Messiah is not a Jewish-Christian point of difference. The point of difference is whether Jesus of Nazareth is the Messiah.