You always have the power to accept timelines. And they have the power to fire you. Instead of trying to accept the impossible, I would persist in explaining the reality. They can reject your message, they can reject you, but they can't reject reality.

Be honest and look for someplace better if they refuse to accept it. That is in my opinion the only way to handle this responsibly.

The problem is that everybody has multiple responsibilities: if finding a new job is hard, and you've got rent to pay and a family to feed, you get into the territory of balancing the risks. Even so, I think it's always best to be clear and honest in your communication about timelines and expectations. If they reject them and insist on unrealistic timelines, point out the problems with those timelines, tell them it's their responsibility if it fails, so they can't blame it on you when it does fail.