Getting Past No by William Ury built on some of the ideas presented in Getting To Yes. The book went deeper on the topic of dealing with a difficult counter party who has immediately taken the position of "No" in an argument.
In a simple to follow formula, Ury has laid out 5 steps to the deal with this situation in a negotiation.
The first thing is to not react. When dealing with a person who has taken a strong position. It best to first control your feelings and not become emotional. If the behavior of your counter party is offensive or triggers your emotions, pause for a moment and allow your self to collect your thoughts.
Once collected, begin disarming your opponent by stepping to their side. Listen to them, ask clarifying questions, paraphrase statements and focus on areas of agreement, build on common ground.
After the conversation has returned to a productive level, change the game. Start understanding what their interests are. Most likely they have only shared their problems. Now it is time to understand what their underlying interests are. Ask clarifying questions, the "Why" and "Why not".
Make it easy for them to say yes and hard for them to say no by removing obstacles that prevent agreement, offering multiple choices and building with them on the options that they find agreeable, share credit to reach a solution and ensure that they do not lose face in the agreement. If they continue to show resistance, reemphasize the importance to reach an agreement, share previous agreed upon items and consider sharing your BATNA in a none threatening way.