"Gut" is one of those wonderfully picturesque verbs that can be used metaphorically to mean something related, but still retains the image of its original meaning (to remove the internal organs of an animal).
Other examples of similar metaphors:
The rock band trashed their hotel rooms.
He's just fishing for compliments.
Let's nail down the details of the contract.
Hopefully Cohen doesn't really mean he wants to eviscerate Kelly -- that would be problematic. Still, there are many words he could have used that don't have such violent connotations like, "Let's wreck her," or "Let's ruin her," or "Let's make her pay," or various others.
The fact that he chose to use gut over all the other phrases at his disposal creates ominous overtones which Kelly (and those who support her) might take the wrong way.
[Edit] In the context of the overall discussion, apparently Kelly mentioned something about being "in a shark tank". "Gut" is a verb often associated with the process of cleaning fish, and so its use could be considered a related metaphor (sharks -> fish -> etc.) However Cohen has a reputation for being a vicious and nasty person, and so his use of a violent metaphor like "gut" was probably deliberate.
Best Answer
When someone says "Let's talk___," it means they are suggesting beginning a conversation on the topic of "___"
Consistency can mean a few things, but most likely in this case it means to keep something consistent, as in keeping it the same over time.
For example, if I have just started a new job asa web designer, my boss, while telling me about my job description may say "Let's talk consistency" to introduce the topic of keeping web pages with consistence fonts and sizes.
The exact phrase you gave has been present in many online articles, because it seems to be a common way to title one of such a topic, but I have never heard someone actually say it in real conversation.