Note: I don't think this was intended subtext, but if there is a book making this clear I haven't found any info on it.
In Star Wars, (movies and otherwise) we almost always focus on the exciting exploits of Jedi Knights or war heroes fighting against the Sith. But whenever we do see average people, they are often apathetic to the larger Galaxy. The people on Coruscant barely seem to notice the war and don't really seem to care when the Empire takes over. My theory is that apathy combined with increasing hatred of the Jedi caused Order 66 to be a non-issue.
Let's think about it from some average dude in the galaxy's perspective. Just watching the Holo-News everynight. He sees the Warrior Monks who guide the people of the Republic. The prequels don't go into government functioning that much outside of the Emperor but from what we can tell they are...
1.) Answerable only to the Chancellor and even then might not be willing to submit to his order if they are more powerful. An unarmed Jedi could beat a battalion of elite troopers unarmed and supposedly helpless.
2.) Command the military and get automatic command positions despite no military experience, and the only reason they make effective soldiers is because of their magic powers.
3.) Take small children away from their homes to be indoctrinated into their order despite being to young to make such decisions. Sure their parents give them away willingly, but if that happened in our world, (and we are shown people tend to think the same way in the Star Wars galaxy) wouldn't your thought be "cult"?
4.) They not only can use physical powers but mental powers to change your mind, read your mind, and make people give them whatever they want.
5.) Employed an army of child soldiers given no choice in their service and treated like disposable. In the thousands! This may have been the final straw for the majority of people to start hating them, and ever safe in their temple on Coruscant never noticed how much the public hated this move.
Combine all that and not knowing everything we the audience are privy to and you can see why people would think less of the Jedi. If, knowing all this Palpatine orchestrates a 3 year war that cost billions of lives. He starts ordering them badly or gives them false information for the generals to go on the general public is probably gonna think "Those Jedi are f**kups or traitors". So when the "Jedi Rebellion" starts people don't really doubt that those child enslaving, free-will subverting, sorcerers would try to take over the Republic entirely. Since nobody knows that the Emperor is a Sith this essentially means everyone trusts the man who finally got the jedi out of the way.
What of the incredibly evil child killing you say? Simple, the Jedi Rebellion killed them, or they were caught in the crossfire. The Jedi do all kinds of things to train these impressionable children behind closed doors, whose to say these monsters wouldn't use them as human shields, or kill them so they never become so powerful?
The people in the Star Wars galaxy aren't idiots, they were tired of, (what they thought) was a corrupt caste of warrior monks controlling them and wanted anyone to take them down, or anything to happen to justify their fear. Palpatine decided he was the right man for the job.