My being a tribute is correct. 'Being a tribute' is a gerund and therefore a noun. Nouns are preceded by possessive pronouns, not object ones. However, 'me being a tribute' (for example) is probably more commonly used and is correct. Using the possessive pronoun sounds more formal, which seems to suit the style here.

Both "that led to my being a tribute today" and "that led to me being a tribute today" are grammatically correct, but they have slightly different structures. In formal English, "my being" is considered more correct because it follows a gerund form (a verb functioning as a noun) and is consistent with certain grammatical rules. However, in everyday spoken English, many people use "me being" instead, and it is widely accepted in casual language. So, both options are possible, and the choice depends on the level of formality you want to maintain. If you were to use 'he' or 'we' instead of 'I', you would follow a similar pattern: "That led to his being the tribute(s)." or "That led to him being the tribute(s)." "That led to our being the tribute(s)." or "That led to us being the tribute(s)." In these cases, "his being" and "our being" are more formal, while "him being" and "us being" are more casual and commonly used in everyday spoken English.

The meaning of the sentence isn't clear. It's puzzling. It seems garbled. I wonder if it has been transcribed correctly. One reason it is puzzling is that we don't usually praise, admire, or give thanks that some country _lost_ a war--although it's possible. "Tribute" is a complicated word. 1) A tribute can be a statement of deserved praise and admiration. "Lincoln's speech was a tribute to the brave soldiers who died at the battle of Gettysburg." If so, a speaker _gives_ a tribute; a speaker can't _be_ a tribute. 2) "A tribute to" can mean "owing to" or "due to:" "his success is a tribute to his hard work." 3) "Tribute" can also mean "a valuable member of" or "a valuable contribution:" "The scientist Marie Curie was a tribute to Poland." If the sentence is correctly transcribed, it might be a humorous response to something said before. For example, imagine speaker A introduces speaker B by saying "It is my great pleasure to give you B, a brilliant person, a great soul, and a tribute to his nation," Embarrassed by too much praise, B might make a joke and say something or other "led to my being a tribute today." If the sentence is a mistranscription, it is possible that the speaker said something like "...that led to my being here to give this tribute today."

Looks like a quote from "Hunger Games" -- the author didn't write with mistakes, but she's a bit too much with style sometimes.