Some Presidents’ collection of dogs, cats, livestock, feathered creatures, reptiles and other wild things (see https://wetnosecentral.com/other-white-house-critters/) was a ‘way out of the park hit, and others just didn’t bother to come to bat at all (see https://wetnosecentral.com/other-white-house-critters/). No pets at all – or mice – is the exception to the rule.
James Knox Polk – President from April 6, 1845 to March 4, 1849
Apparently, President Polk had no pets.
Andrew Johnson – President from April 6, 1865 to March 4, 1869
During the dark days of his impeachment, it is said that Andrew Johnson left flour out at night for the family of white mice who played in his room. No word on whether they were his “pets.”
Resources: Wikipedia (https://en.wikipedia.org), United States Presidential Pets (Wikipedia.org), Newsmax (https://newsmax.com), The Presidential Pet Museum (www.presidentialpetmuseum)