The last data I read about depredation permits states...

Deer Damage Control Permits. —A total of 456 deer permits were issued in 2012, nearly
identical to the 460 issued in 2011. Under this program, 6,152 deer were authorized to be taken.
This was a 0.5% increase from the 6,124 deer in 2011. Of the authorized deer for 2012, 2,359 deer
were reported harvested (Table 6) for a success rate of 38%. The number of deer harvested in 2012
increased by 1 deer from 2011 under the deer damage permit program; harvest has increased 84%
from the 1,282 deer harvested in 2003. Of the 2,359 deer harvested, 269 were reported as adult
male (11%), 223 were reported as button bucks (9%), and 1,867 were reported as female (79%).

Here's a link to that report.

http://www.in.gov/dnr/fishwild/files/fw-MR_1051_Deer_Damage_2013.pdf

While the overall numbers of deer don't appear to be that high (assuming the numbers are accurate), Jb makes a good point about the number of fawns that likely won't survive after their mothers are killed.