A Rasmussen poll taken a few days ago (and which I am only now getting around to) says that roughly 17% of Americans believe our government has the consent of the people.
I don't think this poll was actually measuring people's belief in the consent of the people for government as it is whether people think the government has done things correctly. When we give consent, it is to particular powers of the government, not particular results. Roughly no one is happy about the massive amount of debt we have, but if you asked people if they support spending on Social Security, Medicare, Defense, Education, and what have you, you'll find support being significantly higher than 17%. You'll also likely find that "consent" given for those programs will be much higher, yet not for the resulting deficits.
Let me put it this way: if you consent to eat like a pig and never exercise, you can't "not consent" to being obese later. It is the logical outcome of the actions you do consent to.
Government has grown so large and pervasive that most people have no idea what they are consenting to. So long as their lives go on as usual, they won't care, as Dahl pointed out in Who Governs? The only real option for "the people" is to 1) stay complacent and happy when times are good and 2) get angry and toss out the bums when times are bad. Problem is, poor decisions made when times are good can have negative impacts later on, but since things are good now, people don't pay attention and intervene. When times get bad, most people don't have a clue why that is, and so they react with passion but without intelligence. This creates a devastating feedback loop in democracy, as politicians that need to be reelected in the short term will favor policies that may be nice in the short term but could be devastating in the long term. Since people vote based on how times feel rather than a more objective, rational basis, this political behavior will be rewarded.
Anyway, I hope that poll is wrong. If 83% of the people believe the government does not have the consent of the governed (or are at least not sure of it) and there hasn't been a revolution, then this country is ripe for tyranny.