Can I waive the two-year physical presence based on my marriage case?

A foreign national who is subject to a J-1 two-year home residency requirement is not eligible to adjust status to become a Lawful Permanent Resident (to get a "Green Card"), such as through a marriage-based application, unless (1) the two-year requirement is waived, or (2) the two-year requirement is satisfied. It is possible in some instances, but not all, to succeed with an application for waiver of a two-year home residency requirement, and often this is based upon the source of funding associated with the J-1 visa. So long as a foreign national remains in valid J-1 nonimmigrant status he/she may remain lawfully present in the U.S. Marriage to a U.S. citizen does not, by itself, authorize additional lawful presence (or employment) in the U.S. Especially since you (justifiably) consider this to be a really important situation, there really is no substitute for you and your spouse to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.