As soon as I title this myth, it's obvious what's wrong with it.
Yet a good two out of three times on the Internet, when I see someone complain that the US is not a democracy, they're not making the pedantic point that it's actually a Republic. They're actually saying "it's not a democracy", and the proof they hold up is that the US isn't doing something that they happen to want, or is doing something they don't want. Invariably, their position has much less than 50% support.
Probably the most common "proof" of the non-Democratic nature of the US is the ongoing war in Iraq. But even now, with the low approval rating of all concerned, the War continues to have 30-45% support among the people. (It depends on how you ask the question; there's a continuum of opinion and I don't have enough info to guess the exact distribution.) One of the effects of being a "Republic" and not a "Democracy" is that even 30% support can be enough, though that is pretty fragile, as you can see in the news as I write this.
While I always see this in the context of things not being "Democratic", it's worth pointing out that there is no system on Earth where you always get your way. Even supreme dictators find themselves constrained by politics, not to mention the laws of physics, economics, and mortality (not a typo for "morality"). Complaining that the US isn't a Democracy because it isn't doing something economically questionable or impossible that the complainer wants is a popular one, too. Dubious programs for ending poverty or unbelievably permissive total free health-care programs are popular issues.
If I had to guess at the root cause of this myth, I'd guess it's because ideologies tend to clump together geographically and electronically on the Internet. It's easy in many communities to run through entire days or weeks without engaging with anybody who disagrees with you on some issue. (Blog posts pointing at the allegedly-stupid bad guys that tell you in advance what opinion to have don't count as "engaging".) This creates the perception of 100% support, and obviously, if a policy has 100% support and yet isn't enacted, it's not a "democracy". 100% in your community is of course quite different than 100% in the country.
This is a late entry to the Government Myths series.