Does "won big the day" grammatically correct? Shouldn't it be "won the big day"?
Yes, this phrase is considered grammatically correct within the sentence. If these four words alone were the complete sentence, then yes, the sentence wouldn't be grammatically correct. However, since there is more to the sentence than just "won big the day", it is grammatically correct. It's an informal phrase that means to win a lot of something. He is singing about how he achieved a prize the day he met this person. If this sentence was changed to "won the big day" it would change the meaning of the sentence. The sentence would now mean that he achieved a prize for an important day. Ex: She won big the day she had her first child. Ex: They won big in Vegas.