核心问题
Quite a few people I've spoken to are of that opinion. 照我的理解, not a few, quite a lot 是“很多”“大量”的意思, 而 a few = a small number of, 再加上一个加强语 quite, 其意义应当是“很少”, 即 not a few 的反义词。
词典解答
quite a few 不是表示“很少”，而是表示“相当多”“不少”的意思，但是还算不上“很多”（many）。quite a few 如同 quite a bit, quite a little, a good few(不少)一样，其形式与内容似乎是相矛盾的（似乎不合逻辑）。但是，有的著作解释说，这里是用了“反语”这一修辞手法。这样一解释，它们就是合乎逻辑的了。它们不是 not a few 和 quite a lot 的反义词，反而是 not a few 和 quite a lot 的同义词了。
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Quite a few people have caught cold in this bad weather. 在这样的坏天气里不少人得了感冒。
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We still have quite a few more miles to go before we reach New York. (DAI) 我们尚须再走不少英里的路,才能到达纽约。
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A good student spends quite a few hours in studying, and a good teacher spends quite a little time in preparing a lesson. (IME) 好学生要把许多时间用在学习上，好教师要把许多时间用在备课上。