Fox News has deliberately positioned itself as a partisan news outlet. While their motto is "Fair and Balanced", not even frequent viewers really believe that their take on the news is open to all points of view.
In fact, Fox News was denied a license to broadcast a mixed Canadian/US news channel in Canada due to “broadcasting false or misleading news.” (After plans for a joint channel were dropped, Fox was given a license for their American news channel to be on cable.)
A business strategy centered around a conservative audience means that slamming democratic leadership is a must. It panders to the audience and infuriates liberals, which further panders to conservatives.
While the operators of Fox may not have personal opinions about Obama, it is likely they have hired Obama haters and encourage an extremely outspoken and conservative environment around the workplace. Insiders have reported as much