I am not sure that I can answer your question in the context of an internet meme. In the UK, and I imagine other English speaking nations, we often use the phrase "do not have the time for" something to mean that we don't care for or want something. It can also mean that we do not like something.
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She is using slang words to explain that she has bronchitis and the fire was so sudden. So, she doesn't have time for all this headache and disruptive act.
It's the way she says it that is funny. She speaks from her heart and is totally being herself on live TV.
That's what is funny.
Sweet Georgia Brown