Learn English – “Once upon a time” vs. “a long time ago”

"long" is an adjective. "time" is a noun, as well as the subject, while "passing" is a present participle, the verb.

"Long time passing" refers to a great amount of time that has passed by since the flowers were gone. This can be seen by the fact that the fourth line "Long time ago" indicates something that has happened in the past.

Most songs don't have a correct grammatical structure, and this one doesn't really have one either. I think the correct form would have been:

Long time passed.

But because a song needs a rhythmn, an additional syllable had to be added, hence the "passing".
Of course, he could have done:

Long time has passed.

From a strictly grammatical point of view it is ambiguous. However a native speaker would only use the phrasing "for a long time" if they meant that they had worked here previously but it was a long time ago.

If the other interpretation was intended they would say:

I haven't worked here for very long.