There have been a lot of laughs about the term "alternative facts" (as used by the incoming US administration), but are there logical or philosophical frameworks for the types of distorted truth-telling that may go on in a typical political discussion?
It seems to me that the amount of outrage over that phrase by Kellyanne Conway is entirely for political reasons.
If you are from the political left you are likely to be outraged. If you are from the political right you are likely to rationalize and dismiss it.
For example, one can argue that all she meant was that Sean Spicer's statement was based on evidence and numbers that she trusts and that the interviewer disputes.
It does not even have to be a case of "distorted truth-telling" for she may have said it in good faith.
One can just as well criticize Chuck Todd for ridiculing and insulting Conway based on the evidence he had at the time.
Neither Conway nor Chuck Todd who interviewed her had access to the fact of the matter concerning the number of people who attended the inauguration. Most of the inordinate amount of analysis of evidence as to the number of people who attended the event probably followed the interview rather than preceded it.
That said, it seems to me that the framework you are looking for is epistemology:
Defined narrowly, epistemology is the study of knowledge and justified belief. As the study of knowledge, epistemology is concerned with the following questions: What are the necessary and sufficient conditions of knowledge? What are its sources? What is its structure, and what are its limits? As the study of justified belief, epistemology aims to answer questions such as: How we are to understand the concept of justification? What makes justified beliefs justified? Is justification internal or external to one's own mind? Understood more broadly, epistemology is about issues having to do with the creation and dissemination of knowledge in particular areas of inquiry.
It seems to me that there is indeed a serious problem for people to communicate knowledge, opinion, and ideas. However, it is not especially a problem in the field of public opinion as you write, but also in academy and science, and it seems to me that people have a hard time communicating ideas in general. "Facts" are often just weapons in the war of ideas.
Philosophers are not exempt from these wars either, and their fault may be even greater than anyone else's since you would expect them to know better:
It is just astonishing to see how often "academic" discussions of phenomenological controversies degenerate into desk-thumping cacophony, with everybody talking past everybody else. (Dennett, Consciousness Explained, p.66)
Finally, here is an interesting paper on the subject by Peter Van Inwagen: Is It Wrong, Everywhere, Always, and for Anyone to Believe Anything on Insufficient Evidence?
You can find more by searching for philosophy and disputes, epistemology, etc...