Not so much support, I'd say - but rather indifferent or "gotten used to it" to the point that it doesn't seem to be a problem in their view. It is much closer to apathy and ignorance.
There is a bit of a generational gap at play here. Most millennials were brought up in rather comfortable conditions. Food, health, stable life, education -- for them this is the world how it always have been and always will be. Fascism, world wars, dictatorships -- all that is a distant news on tv (that they don't even watch or have) or in history books (books? what are those?)
Also, with the never-ending facebook newsfeed, that automagically shows them things that they already agree with, fewer and fewer want to leave that bubble.
In other words, millenials are ok with total surveillance because they do not fathom the real implications of what survelliance state is going to be. They have nothing to "compare it to", no intuition, nothing to relate to. For them it will "never happen".
... which means when it happens, it will be really, really bad. It is akin to having early symptoms of cancer, but if you have never been close to such tragedy in real life, you just go on ignoring the symptoms, go on until it is too late.
I guess it is a fate of every generation, some kind of 3 generational "gap":
1st generation - experiences it, puts in laws and organizations to prevent it from happening in future (examples are United Nations after WW2, nuclear non-proliferation treaties between US and Soviet Union, etc.)
2nd generation - happy / golden generation that still knows remembers the lessons of the 1st one and enjoys the safeguards instituted after the events that are keeping them safe.
3rd generation - decadence and calm before the storm. No one is alive from 1st generation to tell them the horrors of the world wars first hand. 2nd generation are "old timers" and essentially ignored. Personal experience of the 3rd generation is comfort, convenience and never ending entertainment.
For the lack of a better metaphor: Winter is Coming.
It's called the Three Generation Rule, and it's no small part of why I've personally taken it upon myself to try to find a way to make sure any kids or friends I come in semi-regular contact have acquire appreciation for how current infrastructure was arrived at, and understand that none of it is a given.
Unfortunately, I'm not the most successful at it, because I'm pretty sure taking the time to collate all this information on the infrastructural pedigree of modern life in your head tends to come with a tendency toward hermitude.
Also coincidentally, hardly anyone seems to want to know about it.
1) That would make the previous 3rd generation before this current iteration (one cycle ago) the generation that experienced WW1 - they'd hardly be ignorant of the horrors of world war.
2) Boomers (your 2nd generation) went through Vietnam and the cold war, so I'm not sure they often felt like the UN was safeguarding them from, well, anything.
3) Boomers also seem to be indifferent and apathetic about climate change, so I'm not sure how that really fits into the narrative.
The most likely answer is that most people just feel indifferent about things that feel out of their control. Boomers likely didn't spend every waking minute about how close they were at several points to being ended by thermonuclear war.
Hell, even for the greatest generation (well, except for Murrow obviously) let McCarthy run rampant right after WW2 until he tried to go after the army.