Or has at least happened once?
http://www.theguardian.com/society/2014/mar/27/first-documented-cat-human-tb-infection?CMP=twt_gu
QuoteTwo people were found to have developed active TB after close contact with cats last year following an outbreak involving nine animals in west Berkshire and Hampshire. They are said to be responding to treatment. Two other people were found to have latent TB, meaning they had been exposed to the disease at some point but it was not active.
The outbreak of the disease in cats, caused by a strain known as Mycobacterium bovis (M bovis), came to light via a veterinary practice, and led to screening being offered to 39 people, 24 of whom accepted. Six of the nine cats were put down, three were treated.
Yet another exciting advancement in the field of Let's Kill the Humans! :D I think it's all part of the eventual feline uprising. My cat Ma'at has been giving me the hairy eyeball ever since I refused to fish her catnip mousie out from under my couch for the eleventh time in ten minutes. I know she's plotting evil. It's either TB or peeing on my yarn.
Uh oh. We better get the government to start shooting cats (http://www.theguardian.com/environment/2013/aug/27/badger-cull-gloucestershire-somerset-nfu), then.
They've already got whole families barricading themselves in the bedroom in Portland. (http://news.yahoo.com/house-cat-oregon-attacks-baby-traps-family-bedroom-005227176.html)