Program mode can be adjusted to find an equivalent exposure resulting by rotating either the main or sub command dials. This puts the camera into Flexible Program mode denoted by P*. (Page 75,Nikon D600 User Manual. Make sure your exposure meter is active (if it shuts off, it may not shift the exposure; also make sure you did not lock exposure or have movie live view active. (Page 319, D600 User manual)
Auto mode will do the same as Program without the ability to shift exposure; AND will pop up the flash if the camera algorithms determine it is needed.