Spot on - I've been in a few of these meetings in my time. I've learned there are two viable ways to respond to requests like that.
The first - for situations where it is truly impossible - is to simply say can't be done, impossible, I'm the expert, end of story. Whatever you do, don't try to explain why it's impossible. All that does is invite further uninformed discussion and opinion around the topic, which either ends up back at the start (it's impossible) or with you stuck having to attempt the impossible. Do this a few times - and only in situations where it is truly impossible - and people will tend not to attempt to argue as much and start to accept your word as the expert.
The second - for things that are merely highly impractical rather than truly impossible - is to say "Sure, lets do it" and immediately shift the focus from the task itself to the time, resources and cost necessary to pull it off. It's amazing how quickly "vitally important" features become unnecessary (or significantly simplified) when you mention the cost or shift in critical timelines. You're shifting the difficult part of the task from something they don't understand (the technology) to something they're comfortable with (budget/project management). I find in this approach it can actually be beneficial to enthusiastically support the request - that flips it from an antagonistic situation (you vs. them fighting over the task) to one where you're both on the same side but you both have to live with losing out because the budget just isn't there - and they're the one who decides it's impossible rather than you.