Elections are around the corner, and Erdogan's approval ratings have been dropping even before the earthquake. Just saying...
It’s possible that a state of emergency on account of the earthquake will postpone the elections.
A leader that actually cares but is overwhelmed would probably not be afraid of admitting that, s/he could rally the population together to overcome the tragedy despite their lack of resources. I think Dubya managed to convey this with 9/11, no one really knew how bad decisions by his administration lead to the threat being unnoticed. Meanwhile with Erdogan, he's been the boss for many years, the public probably thinks: The government's not able to rescue people effectively? Well, that's because it's been a kleptocracy for a long time.