We have available appointments today, however when a patient goes to our website (Appointnow) and chooses ASAP, todays appointments are not offered?

The # of Days Allowed to Search from Current Date (AppointNow Only) for available appointments may be adjusted by the administrator at : 

Setup / Offices  / Office Setup / Select the Office / Edit Office / Click the Advanced Tab 

See the # of Days Allowed to Search from Current Date (AppointNow Only) field and  enter '0' and Save.