It's worth remembering that Obama was also told no at first when he asked for a secure Blackberry. He only got one a few months later after making it clear as CIC he would get one or else.
So they made him one. Well why can't they make two? Or 20?
One answer might be bureaucracy. The NSA reports to the President, not State, so maybe they won't do as much for State. Turf-fighting is pretty common among federal agencies, especially those with overlapping jurisdictions.
Another reason might be that information collection is prized much more highly right now in the federal government that information assurance. Even if the NSA helps out State IA, will they get much credit for it? No. And will they get punished if they fail to help State IA? Obviously not.
Simply put, federal IT is very sick right now. The Clinton email saga is a tiny symptom of that. Snowden and the OPM breach are much larger and more consequential results of this pervasive problem.