1
general::
Proceed very cautiously, as in I knew I was walking on eggs when I asked about the department's involvement in the lawsuit. This metaphoric idiom transfers walking on fragile eggs to discussing or investigating a dangerous subject. [First half of 1700s]
American Heritage Idioms
2
general::
Phrase(s): walk on eggs [and] walk on thin ice
Fig. to proceed very cautiously; to be in a very precarious position. (Fig. on the image of someone walking on something that offers little support and may collapse at any moment.) • I have to remember that I’m walking on eggs when I give this speech. • Careful with radical ideas like that. You’re walking on thin ice.
McGrawhill's American Idioms And Phrasal Verbs