The problem is when people start trying to change the plan half way through execution, non tech people will constantly try to do this because they are clueless its the project leads job to tell them no.
When your manager asks you "if anything can be done to pull those dates in." you say "no" problem solved, until your line manager goes to the big boss who asks the same thing and do you know what your answer is? Thats right its "no". When the big boss says you have to do something then tell him "I cant magic more time you need to cut features", big boss and manager will argue their point but unless you can do magic your point remains the same.
I know its scary being blunt with your big boss but as a senior developer thats your job.