What part of speech does 至少 belong to?
In the book 汉语国际教育用词语声调组合及轻重音格式实用手册, p.241 (which is rumored to be the post-reform HSK replacement), 至少 is classified as a 副词 (adverb).  Furthermore, it's considered a 程度副词 (adverb of degree) in the book 现代华语概论.
In English, we might describe it as an adverbial since it can affect a whole phrase.