Unfortunately, in the general U.S. culture almost any quote from a television show or movie is more likely to be recognized than a quote from a book, unless the book is extremely famous or (as others have mentioned) is routinely assigned in schools.
Most people would recognize quotes like "Call me Ishmael", or "It is a fact universally acknowledged that a single man in possession of a good fortune must be in want of a wife", because both Moby Dick and Pride and Prejudice are very often used as assigned reading at the high school level.
If Woolf, on the other hand, is assigned at all it is far more likely to be at the university level, and then only in courses taken by people focusing on British literature, or twentieth-century literature, or women writers, or some other course usually taken by students who plan to make English lit. a major part of their curriculum. People taking only the general literature requirements are less likely to encounter her writing, and thus less likely to recognize a quote from it.
And, of course, a lot depends on when you went to college and what your literature professors' favorite line of country was. I had a strong focus in English literature, but it was thirty years ago at a small and extremely conservative college -- with the result that we read almost entirely in the works of dead white men, except for Austen and Bronte (who were safely back in the far 19th century when women knew their place). Flannery O'Connor was the sole twentieth-century exception, and that was because she was a strong exponent of the school's approved religious thought (white conservative evangelical Christianity).
Hence, although I'm fairly well-read, I'm likely to miss even direct quotes from anybody writing later than about 1950, or who wasn't white or male. I suspect that I'm not the only one this has happened to, even without a strong religious component to the school.
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Most people would recognize quotes like "Call me Ishmael", or "It is a fact universally acknowledged that a single man in possession of a good fortune must be in want of a wife", because both Moby Dick and Pride and Prejudice are very often used as assigned reading at the high school level.
If Woolf, on the other hand, is assigned at all it is far more likely to be at the university level, and then only in courses taken by people focusing on British literature, or twentieth-century literature, or women writers, or some other course usually taken by students who plan to make English lit. a major part of their curriculum. People taking only the general literature requirements are less likely to encounter her writing, and thus less likely to recognize a quote from it.
And, of course, a lot depends on when you went to college and what your literature professors' favorite line of country was. I had a strong focus in English literature, but it was thirty years ago at a small and extremely conservative college -- with the result that we read almost entirely in the works of dead white men, except for Austen and Bronte (who were safely back in the far 19th century when women knew their place). Flannery O'Connor was the sole twentieth-century exception, and that was because she was a strong exponent of the school's approved religious thought (white conservative evangelical Christianity).
Hence, although I'm fairly well-read, I'm likely to miss even direct quotes from anybody writing later than about 1950, or who wasn't white or male. I suspect that I'm not the only one this has happened to, even without a strong religious component to the school.