Considering the age of the Republic and how little time he'd have to do this (it'd pretty much have to be the first thing he does, and then keeps doing for 10 years), I don't think that's a long enough time to ramp up that level of complacency with his work. The senate is watching, if for no other reason than to justify their own jobs, but there's a lot of them, Valorum was voted out in an exceptionally short amount of time for simply not taking more action.
However, I think there are a few factors that would make this kind of thing possible:
1. If Palpatine could lure the general population into complacency with prosperity and comfort, then most people will become completely self-centered and won't care what their government is doing unless it directly inconveniences them.
Scale it up though, we're not talking about a little graft here and there, we're talking about 20% or more of the entire Republic government's money to pay for what to them looks like nothing at all. Hitler grew to power because the German people were poor and angry after losing WW1, they weren't fatcats, they started depressed and weak and became engaged and energized, ready to blame someone and take something.
2. An all-powerful, central, unified government is ripe for corruption to grow unchecked. This kind of government is accountable to no one (remember the citizens have been turned into fat, contented cows happily grazing on the government's feet) and can literally get away with whatever it wants. Just think of Nazi Germany, imagine if their had been no Allied forces to confront them and hold them accountable for the Holocaust. If we had had a centralized, all-powerful, one-world government under Adolf Hitler just think of what kind of horrors our entire planet would be living under right now. This is why a unified, one-world government is NEVER, NEVER, NEVER a good idea. Because when that government becomes corrupt (it's not even a question of "if"), then you would actually have to leave the planet to escape the tyranny.
That's a big "if", we don't really know that's what he was doing, if he was really fogging their minds. I always took it to mean that Palpatine had used politics to manipulate the people against the Jedi, and with the people's will guiding the Force away from the Jedi, it weakened them.
3. Also, if Palpatine was powerful enough to fog the Jedi's minds... every single Jedi, for every waking moment, for over ten years, no matter where they were in the galaxy.... then just imagine what he could do to the minds of normal citizens. I think it's called the Plot-Hole Steamrolling Power of the Dark Side. Which is a pretty convenient power to give your main villain if you want to gloss over the fact that none of your heroes do anything that makes any sense whatsoever.