1. Achieve the target reductions the CEO is asking for (most people stop right here).
2. Clarify the mid- to long-term strategy for competing successfully.
3. Conduct a thorough and unbiased analysis of the options.
4. Provide a comprehensive assessment of the near- and long-term implications of the cutting alternatives.
5. Preserve your credibility. Live to fight again another day.
If you're not thinking about all five points, you're likely suffering a very slow death by 1,000 cuts yourself.
Third, frame your cutting analysis on the basis of strategic dimensions of competitiveness, NOT on the basis of what's easiest to cut (e.g. travel and outside contractors), and for heaven's sake do NOT cut proportionately across the board (which strengthens the hidden weaknesses in your plan while weakening the strengths). Think about the relative value/importance of customer segments; product groups; channels; or even geographic regions. Consider the marginal returns of a dollar spent in each one. Cut ruthlessly from the bottom of the importance rankings.
Fourth, engage people in finance, sales, or SBUs in your thought process. You have nothing to gain by being an island now.
Fifth, get comfortable with making educated guesses on expected impacts. You're beyond the point where data-driven analysis is likely to help. Think about using monte carlo simulation and other probabilistic assessment methods to make intelligent guesses now (and loop back to "fourth" above).
Finally, present your findings with passion, but not bias. The time for "I believe..." is past. The mantra of the moment is "Having run many options by the good people in finance and sales, we all feel that the smartest course of action is..."
And by the way, NOW is exactly the time to begin building that measurement capability you really wish you had over the past few months.