Your loyalty should be to the company, not the person. So by just "falling in line" you are failing the company.
Remember, if the project fails (and it will fail if it is impossible) people get fired anyways. Sure, getting fired later is better than sooner but it is still gonna happen.
[0] In your exact case, find out what they are actually after. Sounds like it might be a budgeting problem and they only know how to pull a few levers. They're business people, not technical people and they're working in a world that is highly technical. They're really a fish out of water and they don't know it[1]. It might be greed or panic too, which are harder to deal with and in those cases yeah, you should start looking for new work.
[1] I'm not saying a techie as a CEO or in a management position wouldn't be a fish out of water either. That'd be similarly as naive. But a well functioning workplace has to understand that these are different skillsets and we have to intermingle. You can't know everything so we have to work together to leverage our niche expertise.