Kinda? I know that's the supposed cliche, but it doesn't really ring true. The "people's" will as defined by some collective subset of the population has certainly been a powerful influence at times, but it's far from a concept that is simply "given by the people." I don't think Pol Pot's power was given by the people. Hitler's wasn't. Xi Jinping's isn't.
And even Nancy Pelosi's isn't given in the way you imply. Through a strong network of bribing and brainwashing, our entire political system leaves us with the choice of empowering corrupt militaristic theocrats or a party that mostly uses tax dollars to bribe voters. I think a very good response to this situation is "I don't like what Pelosi is doing, but I would really hate what a republican would do in her place." And that doesn't sounds like people have much power at all.
[0]. https://en.wikipedia.org/wiki/Beer_Hall_Putsch [1]. https://en.wikipedia.org/wiki/Enabling_Act_of_1933
I think it's pretty rough to say Hitler was given power from the people in the sense that Rousseau would use the phrase.