KJV Matthew 26:38 Then saith he unto them, My soul is exceeding sorrowful, even unto death: tarry ye here, and watch with me.
MGNT Matthew 26:38 τότε λέγει αὐτοῖς περίλυπός ἐστιν ἡ ψυχή μου ἕως θανάτου μείνατε ὧδε καὶ γρηγορεῖτε μετ’ ἐμοῦ
The phrase "ἕως θανάτου" only occurs in Matt 26:38 and Mark 14:38 in the NT. It might be an allusion (including the reference to "soul") to Isa 53:12, "poured out his soul unto death".
BDAG specifically lists Matt 26:38 and Mark 14:38 as their first meaning, "termination of physical life, death - (a) natural death". They then list their translation of these verses as, "sorrowful even to the point of death".
While this phrase, "ἕως θανάτου" only occurs twice, very similar phrases with very similar meanings also occur in the NT.
- Phil 2:8 - [Christ was] obedient unto death ("mechri thanatou")
- Phil 2:30 - [Epaphroditus came close] unto death ("mechri thanatou")
The opposite of this idea is also discussed in John 5:24 where Jesus talks about proceeding out of death to life as a result of His work and message, by faith. However, this is almost certainly talking about eternal death (Rom 1:32, 6:16 etc) as distinct from physical death.
This, our passage in Matt 26:38 and Mark 14:38 suggests that Jesus' was so crushed that he almost died in the Gethsemane before proceeding to Golgotha. This is discussed at some length in Isa 53 (which I take as a Messianic chapter) with statements like, "he … carried our sorrows" (v4); "he was crushed for our iniquities" (v5); "The LORD has laid on him the iniquity of us all" (v6); "he was oppressed and afflicted" (v7); "it was the LORD's will to crush him" (v10); etc.
From this I take the Gospel record to mean that Jesus bore all our sins and almost died in the garden. He was thus "despised and rejected by men, a man of sorrows" (Isa 53:3). This was dramatically fulfilled in Gethsemane. As bad as Jesus suffering on Golgotha was we should not forget the struggle in the garden as he decided to drink the cup (Matt 26:36-43).