No, at least in the UK, it's easy to find bargains. All mine come from eBay, and I invest perhaps an hour a week finding them. Log in, go to the bikes section, and sort by price. I then work through all of them from 99p to £50, generally, and I look at anything which the title makes sound interesting, and anything where the title is unclear (there's nothing like "racing bike", or "gents cycle" as a title to get my blood racing - who else is gonna even look?).
Everything that looks remotely interesting, if it's somewhere I can pick up, or if it's got shipping, I watch it. If I'm being scrupulous, I'll probably have 80 items being watched at any time, but I know that 90%+ of those are going to go out of my range - no problem, it's the other 5-10% that interest me. Every morning, I glance at what's ending today, and if any of them are still within my budget, I'll fire up Jbidwatcher (it's free, google it). I add the auction, and tell it how much I want to pay, and in the last 10 secs, it bids for me. Fantastic!
The best bargains are usually bikes that are pickup only from the middle of nowhere, and of course, I only get the ones that are near somewhere I have to go, but hey, this guy only wants ONE bike! I've had a Gazelle Trim Trophy, which is a second from top of the line early 80's road racer, for £21, the Raleigh Royal tourer mentioned for £22, an Olmo for £4.20, various Freddie Grubb, Holdsworth and Claud Butler bikes for £20-50, a Raleigh Gran Sport for £60, a Dawes Galaxy for £60, a Mercian mixte for £30, I could go on and on. It just requires a little commitment, and to not be looking for something specific. I'll admit, however, that I don't know whether it would work as well in the states.
What I know for sure is this. I'll take an entry level downtube friction shift over an entry level indexed brifter or thumbshifter system every time. If you're buying bottom end, get an old one! I'll admit, however, that if your budget will stretch, a midrange LBS bike is a good idea, but you'll not get anything with the character of some of the bikes you could find by hunting.