I can only speak for my own experience in my department, but here I'm fairly certain breadth would not hurt you. Two ways (tenure track) applications tend to get looked at are

- are the letters exceptionally strong, written by authorities with detailed knowledge of your work? This is independent I think of breadth, you just need to have to chose letter writers very wisely. For example, it might help to have letter writers who understand the different communities. eg I wouldn't know what FOCS is or know how to evaluate journals in specialties far from mine, but a letter writer would do well to mention the importance/selectivity etc of publications since letters are read by a broad range of people, and it might not hurt to mention this to letter writers!

- do the interests of the candidate fit our department? this often means a combination of having some areas of significant joint interest with a significant segment of the faculty, while helping to broaden our faculty in new directions. Here breadth would certainly help!