We haven't gotten a clear explanation yet, but based on a lot of clues and hints Tsukasa may or may not be actually immortal, and specifically someone directly related to the Tale of Princess Kaguya, possibly even Kaguya herself. You can check wikipedia https://en.wikipedia.org/wiki/The_Tale_of_the_Bamboo_Cutter for the full story but the TL;DR was in the previous chapter (141). Kaguya was actually from the Moon thus explaining why the little girl in this story (Tokiko) wanted to head to the moon to see if there was actually anything there for Tsukasa to head back to.
As to what's likely going on in this chapter: before Nasa conks out in chapter 1 and 2 you may have caught that Tsukasa saved him by taking most of the force of the blow from the truck. She was bleeding in chapter 1 and wasn't bleeding in chapter 2 (more proof of immortality). He then conks out after he tells her he'll marry her.
Here's my guess as to what happened before he actually blacked out:
Nasa likely said something along the lines of saying he'd be with her until the day he dies. Tsukasa rebuts saying something like that is a remarkably short time. Nasa responds saying that even if he dies he'll stay with her forever. Tsukasa questions him saying something like eternity is a lot longer than you'd think, and Nasa confirms/repeats his statement that he'd stay with her forever, no matter how long that may be.
This is why Tsukasa was wiling to marry him despite not knowing much about him, having wandered the earth for 1000s of years already alone and looking for someone who was willing to join her, even if it meant drinking the elixir of immortality.
Purely speculation but it would would explain a lot about the start of the series, these recent few chapters, and would offer a route for a perfect ending where
Nasa unknowingly makes the same promise he made while falling unconscious in chapter 2, reaffirming for potentially the 3rd time that he is willing to stay with her forever no matter how long that may be.