The "degree of bias" is not the variable that you would use, it would actually be the degree of impact on the actual voters and non-voters that participate in political discussions. As you have alluded, it is a figure that is beyond the capabilities of us on this forum to calculate.
In answer to your question, "Do you believe that if all the MSNBC viewers who support Obama started watching Fox, they would stop being Obama supporters or vice versa?" The answer is that some, not all, would be influenced over time by a biased media that is not adhere to the basic fundamentals of journalism. You can see that if you look at our history, even over the last few years.
On the second question, "does the administration get scrutinized and are the results easily available to the public?", the initial answer is yes, there is always someone looking closely into everything, and the data is usually available to the public; however, the discussion is about the mainstream public large media organizations, not small, independent ones. These large organizations have been avoiding some topics (like Benghazi) in the WH press conferences, and they have repeatedly (see the CNN video that I posted earlier) manipulated their "interpretation" of stories and events and the amount of their coverage of these stories/events to fall in line with the current Administration. This should concern you, as a free and unbridled press is one of the cornerstones that our forefathers based our American way-of-life upon.