I've had a lot of experience outsourcing projects and also have a team of 45 guys in house doing SEO, design and programming.
If you go with a provider in Elance, or Rentacoder or Odesk that is very highly rated you should be ok. But when I say high ratings I mean a lot of ratings and almost all of them 10 out of 10.
If you go for guys in India that have reasonable ratings you still might end up tearing your hair out.
I don't think you can get any better than these three sites. I've tried pretty much all of them, and these three seem the best.
Elance - slightly higher prices, but more reliable providers
Odesk - more focused on hourly work. If you don't have specs that are accurate with all of the small details then you might be better off doing hourly work anyway. It's so difficult to get the specs right. As you start to use your web site you will notice things that you didn't realize when you first thought of the project and you will likely want to make changes.
Rentacoder - best for fixed price projects. They have a good escrow system which gives reassurance to the providers.
So basically can you get quality at a cheap price (from overseas providers)?
The answer is yes with some caveats.
You are much safer with a US provider. They are less likely to screw it up.
If you go with someone on rentacoder or odesk (or getafreelancer and any of the others) that has no reputation, a random choice, your chance of them doing a good job is probably 20-50% if it's a big project ... in other words an 50-80% chance of them not doing a great job. Those are pretty bad odds. It's it's an easy project, then there should be no problem going with a new provider from India.
However there are ways to manage it so that you can get a large project handled successfully at lower prices. You need to take one of these two approaches:
1) You try out several providers on a small scale and get experience with one who seems great, and then continue with that person.
2) You get a team with extremely good ratings on the site.
If you take one of these approaches your chance of success go up to about equal with the 25k USA provider.
That's my experience after outsourcing literally hundreds of projects online.
I've also put some more information on this page:
http://timemanagement.com/why_outsourcing_doesnt_work.html