Most experienced managers that I've met can work around that sort of comment:
"We need this by January"
"Let's discuss the hiring process for the new team members we're going to need to accomplish that."
"We don't have the budget for hiring at the moment. If more headcount is truly necessary, you are welcome to use your salary to obtain it."
90% of the time, the project arrives lat, but there's no other major consequences and the manager points to this as evidence that you were padding your budget with superfluous resource. 9% of the time, you buy a new web server on your own credit card and the manager brags to his boss about coming in under budget. 1% of the time, catastrophe hits, the company goes bankrupt, and he tells everyone that call for a reference that your incompetence drove the company out of business.
If you think this is hyperbole, a previous employer stated that a competent sysadmin would never lose data, so back-ups were a waste of money and made admins pay for them out of pocket.