You can check USCIS.GOV for the processing times. If USCIS denies your application after May 17, 2014, you will be out of status and will have the leave the U.S. If USCIS denies your wife's application, she too will be out of status. If she cannot leave for health reasons, they will not force her on a plane, but rather, she may be stuck in the U.S. with no status.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
It is unclear why you and your wife have different I-94 expiration dates if she is your dependent. You are typically given 30 days to leave the country after a denial. Your wife will not be forcibly removed but you and your wife start accruing unlawful presence in the United States after a denial, which may create problems with future entries to the United States or may bar you from entering for a number of years, depending on how much unlawful time you accrued. You and your wife should consult with a knowledgeable immigration attorney.