There's this "I have nothing to hide" sentiment followed by blind trusts into officials, their intentions and their alleged protection. I.e. people are scares of terrorism and would like it to stop, so they hope the terrorists will be found by spying.
At least in countries where the terrorism emerged recently, I'd say...
Being "scared of terrorism" is perfectly legitimate even if not underpinned by statistics.
The conversion from that to "so therefore the .gov ought to have powers that amount turnkey ability to violate human rights on a whim" is the problem.
Any "well actually terrorists aren't that big a deal" discussion only serves to bog things down in the weeds and direct blame away from bad people who believe bad things.
Replace terrorism with whatever the cause of the day is, drugs, satanic cults, tax evasion, etc, etc all you want, doesn't change anything. There are people who believe (though they'll rarely admit it when you lay it so bare) that you can take something that is flagrantly bad in its base or default form (like for example letting the government just read everyone's personal communication by default) and think that the fact that because it can be applied toward noble ends then it is a power the .gov ought to have access to by default.
As a European that lived in the US for a long time, a big difference is that there is also a lot of "European Conformism". You don't want to be seen as the weird one protesting things if nobody else does it. It's just easier to go with the flow and accept things.
At least in countries where the terrorism emerged recently, I'd say...