In a democracy, the people are sovereign. Our elected representatives work for us. This org chart for the New York City government has it right: the various city departments are underneath the deputy mayors, who are under the mayor, and at the very top of the chart, above the mayor, are "the voters of the City of New York".
Voting in an election is different from voting in a legislature, because elections are by secret ballot. This is necessary and unavoidable. As corrupt as our elections have become, the billions of dollars spent on political campaigns ultimately have no power over voters beyond the power of persuasion (often combined with deception and fearmongering). The same is not true for the money spent on buying legislators. And if we were to eliminate the secret ballot, electoral voting would become as corrupt as legislative voting, and possibly much worse. Many opportunities would arise to coerce voters with carrots and sticks. (Do you want to keep your job at Wal-Mart?)
So I'm not suggesting that we eliminate the secret ballot. However, we should recognize that it has real tradeoffs.
Legislative votes are public, so legislators can be held accountable for their votes. This can happen in the next election. And even legislators who aren't running for reelection might be concerned about their legacies. But voters have all the power (albeit diffuse over a large population) with none of the individual accountability that would ordinarily come with being at the top of the org chart. The costs of bad decisions at the polls are completely externalized.
This is part of why systems like California's (with more direct democracy) are flawed. Direct democracy sounds good on paper, but the secret ballot means that it lacks the safeguards that representative democracy has. California voters can pass irresponsible initiatives like Prop 13, and then leave it to someone else to clean up the mess.
We can see the negative consequences of the secret ballot in the present debt-limit crisis. If the unthinkable happens and we hit the debt limit next week, then (in the absence of 14th-Amendment remedies or other emergency solutions) President Obama and the executive branch will have to start making decisions about which bills the government will stop paying. The most just way to proceed (if the secret ballot didn't make it impossible) would be to cut off Social Security checks to people who voted Republican in 2010. Why should the innocent suffer along with the guilty?
In the absence of the data needed to implement such a solution, we'll have to settle for blunter instruments such as cutting off all Social Security checks to House districts represented by Republicans until the debt ceiling is raised. Anyone who has a problem with this could contact their congressman.