First of all, you need to realize that the number of resources is almost as important as the percentage each resources is allocated. You have 48,000 hours to complete a project in a little over 6 months. You might start by thinking about that number. Is the requested end date realistic or will you have to recommend to the project sponsor that a different date is required.
Then, you most likely need to sit down with the team leads/PMs and have an up front planning session for each of the projects, working your way back to the end date. This can be a high level plan, perhaps time boxing each project phase for each project. You really need to work out as much parallelism in the projects as you can as the deadline is short. You won't succeed if they all require the same resources and start at the same time.
Once you have an effective plan which the team buys into, you will have what you need to negotiate with resource managers. Right now, without a solid plan, they are legitimately concerned about how the resources will be applied.