This cartoon was published in the May 31, 1862 issue of Harper’s Weekly, which you can read at Son of the South. I think the cartoonist might be lampooning Confederate politicians for thinking about fleeing Virginia as the Union armies approached Richmond in the spring of 1862.
Eventually Mr. and Mrs. Davis made it back to Beauvoir, their home in Biloxi, Mississippi:
Sons of Confederate Veterans publish a site about Beauvoir.