I've personally done this exact thing. If the project is underestimated, there isn't always a solution. I worked on a smaller project for an agency where I was

I've personally done this exact thing. If the project is underestimated, there isn't always a solution. I worked on a smaller project for an agency where I was the tech director. Meaning I had a direct line to clients and account managers at all times as well as authority over the execution. I raised flags when the contract was drafted that it was vague and optimistic, but it got signed anyway. I did a prioritization and forecasting exercise to keep scope in check and set milestones for client obligations that would roadblock us. We could see in real time how far off we were and I reminded everyone at every turn. The account team who sold the project were not involved in execution. I back-channeled to our CTO that they messed this up and we have no hope of delivering on budget. We ended blowing the budget by a mile, the ones that sold the project said the team didn't execute and I got let go. As far as I can tell, I did everything right and still lost. My biggest regret is that instead of insinuating the account team were at fault, I should have yelled it at them.