It is challenging to work with people who are unhappy with their job, the people they have been assigned to work with, or specific tasks that they have been assigned within a project.
If this is the first time that you have seen this reaction, it is perhaps easier to manage. However, if this happens on a regular basis it is probably more challenging to deal with. Clearly, this team member was assigned to the project because of specific skills and knowledge they have so it is important to deal with it early within the project. If this has been a chronic problem you should try to intervene before this team member has a disruptive influence on the team.
You may choose to deal with it in a private conversation or by structuring the planning meetings so that the individual has less of an opportunity to make negative comments. If you keep the meeting focused on the tasks that need to be done, assign tasks to smaller work groups quickly, and organize the work groups so that the disgruntled staff is placed within a group that is focused on getting the jobs completed. Minimizing the time for complaining and report on the positive progress on the project.
Sometimes controlling the environment, creating a positive atmosphere that is focused on the tasks, and asking for feedback on what worked well on the project may begin to turn things around. However, you may also need to be prepared to intervene individually if this plan doesn’t work.