spoken language - Meaning of 一度や二度じゃ、とうてい伝えきれないくらい に

その返事と、その笑顔が、一番たまらなかった。

一度や二度じゃ、とうてい伝えきれないくらいに。

My main confusion is with the 一度や二度じゃ part of the above. The character just confessed his feelings to someone and after hearing her response we see the above. I've looked up and 一度や二度じゃ or 一度や二度では appear to be relatively commonly used in these types of statements.

For example:

初めて訪れた時、一度や二度ではとても回りきれないことを知り、時間がかかってもいつかは制覇しようと思っていました。

This makes sense to me as it means one or two times (of visiting the place). However, I don't quite understand what it means in the context of 一度や二度じゃ、とうてい伝えきれないくらいに. One or two what exactly?

Answer

その返事と、その笑顔が、一番たまらなかった。

一度や二度じゃ、とうてい伝えきれないくらいに。

In this context, 「一度や二度じゃ」 should mean:

"in one sitting or two"

There was simply too much to tell about その返事とその笑顔.

"His/Her reply and smile were so amazing to the extent that I just could not tell you everything in one sitting or two!"