Punctuating a 'plural' quote?

Hi,

I'm writing a personal essay and trying to convey my brother saying "Come on!" to me multiple times. Here's the sentence I have:

As the nagging and the begging and the "Come on, let's go" 's started to pile up, I felt myself caving to his demands.

This looks very awkward (and also, more importantly, incorrect). How do I correctly punctuate the command that my brother is giving me?

Thanks in advance!