^^ I agree with Rob. Local businesses in your zip code usually don't mind price as much as you think. They would much rather care about yourself. In fact, I will tell you that every time I go out and canvas my area I get a job. Sometimes its a little $300 job or sometimes it's over a grand. It really doesn't matter because I'm the only one here going out while everyone else is scrambling to be the top guy on Freelancer (lol).
Also, your services are tax deductible. Despite what the news says about the economy, businesses still have a ton of money and if they don't they have a ton of credit. The vast majority of businesses routinely get faxes for quarter million dollar loan offers in my area, especially manufacturers. So charging $1,000 for a website is nothing to them. They want you to be friendly and solve some kind of problem.
When I owned a physical building I bought from almost every salesman that walked into my door. I bought advertising in newspapers and TV simply because they walked in and asked for the business. I respect (and your prospects will too) anyone who has the balls enough to walk into my store and ask me for money. That takes brass balls.
You're not going to get thrown out and they're not going to be annoyed with you personally. If they tell you to come back later just come back later and go visit another business. Treat it like it's a job. You have to go out selling for 8 hours a day or your boss (in my case, my wife) will fire you. She will divorce you and the judge will order you to pay her all the money you'll ever make and you can't see your kid until she's 18. That's what I pretend when I go out selling LOL!
You can go to the post office website and look up "every door direct mail." You'll get an exact number of how many businesses are in your zip code. Then just go visit them! You can even do an entity search for your state and find out their names for free or simply buy a listing (Info USA or Robert Eagle sells them cheap - Robert Eagle is very price-friendly).
So in that sense saturation doesn't really matter. The people who buy from India and freelance sites are usually government entities or very large corporations who employee corporate buyers to buy on price. If you look at some of the largest companies out there, check out their websites. You'll find that they suck. Some aren't even responsive.
Another thing to keep in mind when selling web design is that you might not actually be selling web design. The customer cares most about what your product DOES rather than what it IS. If the customer already has a website but it isn't mobile friendly, then you now have a hook for them. You say, "hey, I saw your advertisement online. I can double your ad conversions this week." And you do that by making their site mobile friendly and now 62% of surfers can see their website better