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I consider myself to not be a people-person. Perhaps the most effective developers, though, are the ones with the highest people skills - solve their problems effectively (aka - help them help themselves) and you can get back to the cool problem at hand.
If there's a productivity problem and the manager is trying to change things, then I would suggest you rally the troops and gather ideas, present your manager with some useful tips. If s/he is unwilling to listen, take your skills elsewhere. There are better managers. Perhaps more accurate effort estimation is needed - this could be a case of just too much work for too little money. If you don't take action to resolve the apparent productivity problem and hope that the manager "does his job" by taking full responsibility for the productivity problem, then you need to find a new job - the team is broken.
With respect to managers everywhere - a team without a manager is like a team without an objective. Someone has to keep things in check or the customer will no longer pay the bills - and all of your jobs are out the window.
If this is a political problem where the manager is "safe" from ever being questioned, then a mutiny may be at hand for an uninformed/unwilling manager. I've seen it happen to managers who impose nonsense policy on their teams. In this case, the team had very high attrition of the engineering staff.
My credentials: successful professional developer and technical lead for 6 years (getting paid for my hobby - woohoo!), promoted to manager of software development teams for 3 years. Over the course of my management tenure, the team size and budget both doubled roughly with about 12 engineers in the budget before I moved on. Went back to being an analyst/developer because making money was not my only objective. Now I can effectively support my manager with useful feedback that can make everyone on the team successful. I am on a totally kick-a$$ team where everyone respects the others' positions and responsibilities. Play together, win together.