One of the meanings of "cutting" is "reducing", along with the "thin" it makes me guess that it is something in the sense of "that the singer patience is beggining to wear thin". Or that it´s "by a thread" or still that "she/he (the other people) is trying his patience/. Etc.
Another example with "cut the line thin":https://answers.yahoo.com/question/inde ... 834AAwNtxa
You really cut the line thin with the Prom being only three weeks away.(In a way it means "you really are playing with wire/now you really have a tight sked.)
Ah, "sked" is a slangy way for schedule.
"cut the line way too thin"
In Portuguese we could say it´s a "situação em que algo está por um fio" ou "...que se deixou ficar por um fio."