I do have a set of the new iPhone earbuds that I bought to use with my iPad 3. They do work. The 3.5mm is a standard for these earpieces. They should work on your Mini - as long as there is no defect with the earphones or the Mini.
Are you using the earbuds with an iPhone? If you are and if they work, maybe there is something impeding the jack from going into the opening on the mini. Maybe yoy should look very closely at the opening - with a magnifying glass and a flashlight and maybe you can see if there is something in there.
Have you tried any other earbuds with the Mini? Any iPod or iPhone earbuds should work. Any spares lying around the house?