The Jargon File (version 4.4.7, 29 Dec 2003):

juggling eggs
 vi.

    Keeping a lot of state in your head while modifying a program. ?Don't
    bother me now, I'm juggling eggs?, means that an interrupt is likely to
    result in the program's being scrambled. In the classic 1975 first-contact
    SF novel The Mote in God's Eye, by Larry Niven and Jerry Pournelle, an
    alien describes a very difficult task by saying ?We juggle priceless eggs
    in variable gravity.? It is possible that this was intended as tribute to a
    less colorful use of the same image in Robert Heinlein's influential 1961
    novel Stranger in a Strange Land. See also hack mode and on the gripping
    hand.


The Free On-line Dictionary of Computing (30 December 2018):

juggling eggs

   Keeping a lot of state in your head while modifying a
   program.  "Don't bother me now, I'm juggling eggs", means that
   an interrupt is likely to result in the program's being
   scrambled.  In the classic first-contact SF novel "The Mote in
   God's Eye", by Larry Niven and Jerry Pournelle, an alien
   describes a very difficult task by saying "We juggle priceless
   eggs in variable gravity."  See also hack mode.

   [Jargon File]