I just read ten blog articles on the importance of first lines in books. They're important. A lot of suggestions were thrown out. I liked many of the ones they named. I couldn't think of any that stuck in my mind, but I may not be paying attention.
If I'm ready to read your book based on the blurb or excerpt, then you pretty much have me committed for at least the first 30-50 pages (less if it really, really sucks). If it kind of blows, then I'll stop. But as long as I really like at least one character, or the premise, or the story, or the writer's voice - I'll finish it. Some get better as the book goes on, some don't. Some I end up loving after being dubious for the first 50 pages. You just never know. It's only a handful that I don't finish at all - but boy-o, if you are one of them, I will never - never ever - read your writing again. Period.
Back to topic... I read the back cover blurbs, I read the tag lines, but I have never read the first line or even the first few lines and thought, 'Boring, I'll move on'. Many people do, apparently. So, I see the importance. You don't want to lose those readers.
But in all honesty, the first line is important, the first page is important, the first and last lines of each chapter are important. They say that the last page/paragraph/line of your book sells your next book. Don't ask me who they are. So, what part of your book isn't important? You gotta love the characters. The setting can pull you in. The dialogue can be authentic or witty. It all has a place and the combination of these elements is what makes you great or not.
This was compared to pick-up lines in a bar. I get that - to some degree. If a guy walks up and says, 'what's your sign, doll?' - I may think he is a jerk, but if he's cute enough or smells good enough or is wearing the concert tee that I have too - then I may give him a few more moments to prove that perhaps he is just clueless about meeting girls, but has charm lurking somewhere.
I am not dismissing the important first line. I want mine to be great whether it is the basis by which my entire book is judged or not. So, what's the point of my musings? I dunno - maybe that's it, just thoughts. I wasn't consciously aware that first lines mean nothing to me as a reader until I started thinking about this. As a writer, well...that's a different story.