Would citing a political book be considered credible?
I could be misinterpreting your question, but I believe you are running into a difference in the popular (non-academic/scientific) definition of what a citation is for, the journalistic/communicative use of citation, and the scholarly purpose of citation.

In the popular idea of citation, you are citing something to add credibility or "proof" to your argument. For instance, "a medical publication from researchers at Harvard said eating tomatoes increases cancer risk [citation here], so you should stop eating tomatoes." You are citing to be persuasive, by borrowing legitimacy and authority from those that have it and seeking to use it to support your agenda.

The journalistic use of citation, in theory, is to communicate the source of some statement or argument that you are reporting. Done right, this allows people you are communicating with to more easily locate the relevant materials they can investigate further on their own, if they are so interested, as well as to help ensure that the journalist is being honest by making it easy to check their work. 

The scholarly purpose of citation is to indicate the source of ideas and work that is not your own, to make it distinct from your own contributions. This exposes your assumptions, directs researchers to closely related works, and can be used to indicate whether what you are doing is normal (by showing other researchers who've done or found the same thing), or if you need to justify your comparatively unusual practice or findings. It is also used to externalize support - so if you want to use a method because some other researcher's work said that method was useful for the problem you are working on, you just cite that research to support your use of the method. This effectively "includes" their work into yours, without the need for reproduction (copy-paste).

So with that said, let's take your example from a scholarly perspective.

If you make the statement that a US president supports fracking, especially for the purpose of job creation, you should cite why you think that is so - and citing their own book would certainly be a good way of supporting such an assertion. In indicates the source of data from which you draw your assertion.

On the other hand, lets say you want to state that fracking will create more jobs in the United States. While you could certainly cite a political/popular book, the response to that from an academic perspective is simple: the book you cited is just another persons unsupported opinion, and does not indicate scientific or otherwise scholarly support for your statement. The citation does not include research, novel methods, an analysis of an existing data-set nor the collection of new data. In short, it does not support your statement in a scholarly way, and would further make a listener/reader wonder if you know what you are doing at all.

So in the end, what you should cite, and how you should cite it, will depend on what the role of your presentation is and the nature of the argument you are making. If you are quoting something, cite the source of the quote. If you state that so-and-so supports a certain policy, cite the source that establishes that that person indeed does support that certain policy.