2016 blocks = 100800 BTC. At the start of a new difficulty, a dedicated agency like the NSA could probably mine 100,000 BTC in a day. Keeping the same hashrate they could mine another 100,000 in four days at the new difficulty they set. If you doubt this, remember the NSA has their own chip fab...they might have even tested their tech, search for "mystery miner"...
.. which is now less than 5% of the global hashrate of 10 TH. I'm guessing this is someone at Pixar or some other render farm.
To mine an entire difficulty adjustment in a day would take 14 times the current network speed of, or 140 TH, which is 280 times the mystery miner's peak hashrate. We're safe from this mystery miner...