No, you do not have too many teachers. In LAUSD, they will have something like 43 kids to a classroom in high school.
http://laist.com/2009/03/25/lausd_teachers_get_contract_bonus_i.php
That's not too many teachers. They don't make too much money, either. I can't think of a more important job than teaching our kids. My sister in law is a LAUSD sub. She couldn't find work because LAUSD was hiring all their laid off full time teachers to do sub work. That means fewer teachers for more kids.
Do we have too many cops? Again, in Los Angeles, the "austerity" measures took over hundred cops off the beat.
http://articles.latimes.com/2009/apr/01/local/me-lapd1
How that doesn't translate to a worsening city is beyond me.
Obama wants to send AID to the states so that those support workers, cops, and teachers are rehired. So kids can go to school with less than 43 kids in their classes and cops can go back out on patrol.
Romney thinks that's a bad idea and wants to cut them further. I'm not sure how you cut the size of government without firing people.