First, Hathat tip to @David Espina. Everything he says is true. I'm just concerned that it won't be helpful when the project crashes and burns and you're trying to shelter yourself from debris. And, and when you're trying to figure out how to spin this failure on the resume you're preparing for the next job.
I think that you may wish to ask this question on workplace stack exchange, because I think the workplace issues dominate the project management issues.
I'd strongly endorse Mr. Espina's recommendations that you:
- Document and escalate risks. You're in a very good place to assess the likelihood that the project will be X months late because the complexity of tasks have been underestimated. But always do #2.
- Identify alternatives - up to and including preparing an alternate project schedule that you believe is more realistic.
(Aside: In addition, I'd also update my resume and begin the job seeking process, including the small tasks that the PM has assigned (you cite "find a network communications library", etc.).