Arguing won't work. In fact, given the power structure, arguing will simply put you in a worse position. Doing nothing simply delays the problem and you will eventually be held accountable for your perceived failure to meet the stakeholder's unrealistic expectations.
To change a senior manager's mind, you need to change the manager's expectations. Though you may battle a heavy overlay of skepticism, use of effective communication and a planned strategy should do the trick.
Effective communication requires that at least two of the following three elements be present:
• You're known as a technical expert.
• You're credible: People know you provide reliable and accurate information.
• The information you're communicating is relevant to the receiver.
Influencing a skeptical senior manager requires you to boost all three facets. You cannot do this alone. Some options to consider include:
Co-present your case with a trusted source. You increase your chances of success by sharing the stage with someone the executive trusts. Build the value of your ideas on the credibility the co-presenter has established with the executive.
Demonstrate endorsements to build power. Ask others in positions of power to let the executive know they support your idea.
Stroke egos and use the executive's credibility. Authentically move ownership of "the" idea -- not "your" idea -- into his space. You can do this by using phrases such as "You've probably seen this data already," or "I'm sure your analysis has shown similar results."
These approaches need organizing and take time but are essential if you are going to effectively advise upward.
How do you influence your senior managers?
Read more on stakeholder management.