To do paperwork for the administrative side of some business or organization, especially paperwork that is or feels petty, uninteresting, or unimportant. Usually used in the continuous tense. I spent the summer inside pushing paper for my father's construction company to help pay for college. After five years of pushing papers nine to five, seven days a week, I finally decided to quit and pursue my dream of teaching English in Japan.
See also: push
Do administrative, often petty, paperwork. For example, She spent the whole day pushing paper for her boss. [Colloquial; second half of 1900s]
To have one's time taken up by administrative, often seemingly petty, paperwork: spent the afternoon pushing paper for the boss.