"I used... to do all of my writing standing; and I strongly recommend the practice to bother the quill-drivers."
-- What I Remember by Thomas Adolphus Trollope, 1887.
During the Georgian era and on through the Victorian era, the term quill-driver was used in the same way that we today would use the term pen-pusher. It was a well-ingrained bit of slang, as evidenced by its use on into the 1880s, well after quills were on their way out.
The meaning was quite straightforward, and did not change over the nearly two centuries that it was in use. A quill-driver was someone who worked endlessly over a ledger, a common drudge of the most common sort. Obviously, a quill-driver was educated and most likely middle-class, so it was not too strong a term of condemnation, but it certainly wasn't flattering. The first recorded usage of the phrase was actually in the form of 'quill-driving', in 1719:
When Inns of Court-Rakes,
And Quill-driving Prigs,
Flock'd to St. James's,
To shew their long Whiggs.
-- Pills to Purge Melancholy by Thomas d'Urfey, 1719.
With the slow death of quills in the mid-1800s, the term slowly died out. But by the 1880s those crazy Americans had started using the term pencil pusher, and by 1910, pen pusher. We are now in the age of button pushers, and it looks like the appellation 'driver' has faded entirely out of use. Pity.