That depends which day you are talking about. I've got a big day today. I've got a big day tomorrow. I've got a big day on Sunday. "What are you doing tomorrow?". "Gotta big day." 明白嗎？

i think it depends on the sense that they are talking about

"I've got a big day today" means that you are very busy at the office today.[ present tense] "Tomorrow I will have a big day" means the same thing, you will be busy.[ future tense]

I suppose it depends on context, I normally hear this phrase as "I gotta big day tomorrow" "I have big plans" or some variation. Sometimes "Ahead" is used instead of "tomorrow" I think in this situation, it is just used as an idiom. I think it is meant for the audience to assume that whatever will happen will happen in the next coming days, but to translate to other languages that dont use a phrase like this, it makes sense to just add tomorrow.

I'm not sure if there are some words lacking in your sentence... normally, when we say "got a big day", it implies to a big event that will take place ahead (tomorrow or the next following days). however, unless you specify the time you are going to be "busy", it may have different idea. like for instance: "I've got a big day starting now until the next day." thus, the sentence above refers to a very busy day starting NOW (today). :)