If I overstay in USA after coming here on a visa waiver program, what is the maximum time that I can overstay?

Generally, if someone enters the U.S. lawfully and with inspection, such as through the Visa Waiver Program, and then becomes married to a U.S. citizen, the couple may succeed with an adjustment of status application even if the foreign national may have overstayed her authorized stay - even if the overstay is very long. There are many more details that determine eligibility, however, and it would be wise for you and your fiance/fiance to consult with an immigration attorney.