This is from this TED talk: https://www.ted.com/talks/sheena_iyengar_on_the_art_of_choosing/transcript?language=en And yes, what the above people said. "Die hard devotion" is complete, unfailing devotion. She's exaggerating here a bit (most people aren't die hard devotees of a soda), but many do have a preference and, in fact, a strong preference. (For the record, Pepsi is swill :)).

In general "die hard" means complete or total or something that is to the extreme/maximum. For example someone can be a "die hard Metallica fan." Meaning that they LOVE LOVE LOVE Metallica; they buy all their records, go to their concerts, know random factoids about them, etc. Just like some people are "die hard Barcelona" or "die hard Real Madrid" fans. They will only support "their" team. You can also talk about people who are die hard supporters of a particular political movement or candidate: "he's a die hard Bernie Sanders supporter"/"she's a die hard Republican." And, of course it can apply to brand loyalty --someone may only drink Coke and never Pepsi. They'd be a "die hard Coke drinker."

So in the US, many people have a preferred soda (MTN Dew, Coke, Pepsi etc). So if you offer a soda they don't really like it is perfectly acceptable in the US to just say no thank you. We would see every soda and other drink options as a choice Example: Coke, Pepsi, 7-Up, water, milk and juice would be 6 choices. Maybe it's because the US drinks more soda (and junk) than the other English speaking countries. Die-Hard Devotion (in this case) is a phrase that means that you ONLY drink a certain type of soda and no other.