Overextend oneself, undertake too many different enterprises. For example, Tom's exhausted; what with work, volunteer activities, and social life he's spread himself too thin. This expression alludes to smearing something (like butter on bread) in such a thin layer that it does not cover the surface. Jonathan Swift used spread thin in a positive sense, that is, something should occur less often (Polite Conversation, 1731-1738): "They (polite speeches) ought to be husbanded better, and spread much thinner."
With so many layoffs in one's work place there is nothing one can do except spread oneself too thin to keep one's job.