According to the Australian Macquarie dictionary:

cusp
// noun
1. a point; pointed end.
2. Anatomy, Zoology, Botany a point, projection or elevation, as on the crown of a tooth.
3. Mathematics a point where two parts of a curve touch and end.
4. Architecture, etc. a point or figure formed by the intersection of two small arcs or curved members, such as one of the pointed projections sometimes decorating the internal curve of an arch or a traceried window.
5. Astrology the transitional first or last part of a sign or house when the new sign is gaining ascendancy, but the influence of the old one persists: to be born on the cusp. [Latin: point]

It appears that the term has quite a scientific background, but that it is being used in a slightly colloquial sense. The quote you've provided appears to be using cusp in the Astrological sense ie. akin to the word "verge" whereas the general use of the noun cusp would mean the apex or point. The context in the quote doesn't indicate being at a "point" ... yet ...

Anyone else?

Hev