Although you may not yet be at a standoff, you do need to resolve this issue quickly and effectively, to keep the team from losing trust in you and your ability to lead this project. One great way to lose their trust is to ignore the issue, charge on to make the executives happy at all costs, and just try to "fit the 10 pounds into the 7-pound bag." This situation is not uncommon and should be addressed
like any other identified risk. What you need is data, options, and logical, business-based recommendations to resolve this dilemma.
First, walk the team through an evaluation of the project in terms of scope, schedule, and resources to determine what tradeoffs can be made to address the constraint. Start by working with the team to identify what is driving the schedule longer than desired. What options exist to reduce the schedule without adding more risk? Would adding more resources be an option and would it really help? (Remember the adage that nine women won't produce a child in one month—only realistic resource options should be entertained.) What would the impact of those options be on project budget? Would the cost, and any related new risks, be acceptable if the extra resources were provided? Or are there particular scope items or chunks of work that are driving the schedule longer, due to complexity or poor requirements definition or just sheer amount of work to be done? Can any items be partitioned to a future release to allow the project to hit an earlier deadline? If so, what is the impact on the entire set of target customers if those features/functions were not present at release?
Working to answer these questions builds a set of possible alternatives for the project, with data on their impacts that will help you have objective, not emotional, discussions with whoever is pushing for an earlier deadline. You will need to lead the team through a process of trade-offs and optimizations of the project plan to see what it would take. The guidelines and templates in Planning and Scheduling: Make Trade-offs and Optimize can help you through this process. The Flexibility Matrix is a simple but effective tool that helps guide tradeoff discussions on scope, resources, and schedule during project definition and planning work. The matrix is used to clarify which constraints are flexible and which project goals must be held. The results of this activity will provide a set of recommendations from the project team to the executives, showing how the project would have to change in scope and/or resources to achieve the requested earlier deadline.
Your project sponsor should help the team by providing their insights on what tradeoffs might be most palatable to the other executives (or to them, if they're the ones driving for the new deadline!). The project manager–sponsor relationship is supposed to be one of mutual support and collaboration for the good of the project, so take advantage of their help before taking recommendations to a broader set of executives.
Don't expect this to be a simple meeting—or just one meeting for that matter. You may be asked for assessments of other alternatives before the executives make a decision. That is great if it happens—it means they are collaborating with you and the team to solve the problem, not blindly demanding changes they don't understand.