Don't make this a left-right thing. For what it's worth, the people I know most in support happen to be weakly right-of-center and those most opposed are radical leftists but really there are other things dominating (the leftists are nearly tied by some Libertarians). Individuals with fair-weather beliefs are an issue on both sides (and it's somewhat human, unfortunately, which isn't to say desirable). And of course amongst mainstream politicians of both parties, we certainly are seeing a huge amount of fair-weather behavior - with strong supporters of this crap under W. now rallying against it while previously critical Democrats forget what the problem was...
To my mind, there's a few strong points worth making here to those rallying around "their guy"... 1) "you might not trust the next guy/gal" (which gets made pretty often), 2) pointing out that a lot of people involved here aren't even NSA agents but contractors with big defense firms, and 3) there's a documented history of abuses (most of which were found because they were self-reported, so there's tremendously more abuse going on we don't see).
"The upside to having a Republican in the White House, is that vast majority of liberals will finally stop being hypocrites about 'speaking truth to power' and pretending to care about human rights, and they'll instantly get upset about the NSA story (while claiming of course that it was solely the fault of Republicans all along)."
You'll have to explain why it would be different than every other time we've switched parties here. Some of this stuff was talked about under Clinton (e.g. Carnivore, though that was FBI), and some Republicans fretted. Much more was introduced under W. after 9/11, and some Democrats complained. Now Obama has extended it, and Republicans are rediscovering their opposition to this stuff, but they're sure to forget just as quickly if we give them power again. Probably the best chance is to have both houses of congress with an overwhelming majority of the party that does not control the presidency (and it probably doesn't matter much which is which).
There might not be a broad opposition coming from the left but there is an opposition. If it were up to Democrats the bipartisan Amash amendment to defund the NSA would have passed[1]. The problem isn't a Democrat in the White House, it's a non-functioning GOP in Congress.
I still support Obama and I have no problem talking about it.
The upside to having a Republican in the White House, is that vast majority of liberals will finally stop being hypocrites about 'speaking truth to power' and pretending to care about human rights, and they'll instantly get upset about the NSA story (while claiming of course that it was solely the fault of Republicans all along). The Republican President would act as as lightning rod, the perfect excuse to rediscover their fair-weather beliefs. The liberal wing would then apply pressure to the rest of the party to restrict the spying.
There would finally be broad based opposition to the NSA's program from one of the parties.
Unfortunately, Hillary is going to win the next election by a wide margin. And absolutely nothing will change; rather, most of the programs will be permanently codified into accepted US Government practices.