Greetings Corey,
First of all, I would recommend that you verify your verticillium diagnosis with the University of Illinois Plant Clinic http://plantclinic.cropsci.uiuc.edu/
According to most plant pathologists, sanitation and prevention is really your only method of recourse - if and when a positive diagnosis is returned. Based on what I've been able to find, there really are no fungicides available for treatment of verticillium wilt (a persistent, soil-borne fungus). Thus, prune out dead branches as they become apparent - remove severely infected trees. Remember to sterilize pruning tools between pruning cuts. Additional control measures include maintaining adequate soil moisture and fertility around your trees.
Unfortunately, your sugar maple is susceptible to verticillium wilt; however, your white birch should be fine.
Please refer to the following plant report on verticillium wilt from the University of Illinois for more detail and specifics:
http://web.aces.uiuc.edu/vista/pdf_pubs/VERTWILT.PDF