Deadlines often slip. It happens ALL THE TIME, regardless of elaborate and sophisticated project management techniques and skilled contributors. Deadline slippage is also RARELY FATAL, but yeah, leads/PM's can absolutely get themselves metaphorically shot by bearing bad news to the wrong people at the wrong time.
Some orgs hire a ridiculous number of PMP's who pretend like they're making a difference but are really just practicing an elaborate dance of goal-post-moving to appease the deadline-gods. People in such orgs often bullshit about a "track record" of being "always on time and under budget".
Best thing OP can do is learn from the mistakes and speak up next time during planning phases, well before deadlines slip.