The simple answer to the problem of when you can consider your site complete: when it's done.
The more complicated answer depends on one of two things happening:
• You have the site you want.
• You can't afford to pay the coder for any more revisions.
Unless your site simply doesn't work--meaning that it actually crashes browsers when it loads, or that the individual pages don't link together properly--don't be afraid to accept the second outcome. Remember our TV analogy: the ultimate goal of a direct response web site isn't to be beautiful, but to sell a product. Yes, making your site beautiful, intuitive, and efficient can help with this ultimate goal--but it's more helpful to have a website that works and does its basic job.
And remember that you're running a business, not an art museum. The basic rule of business is not to let your costs exceed your profits--and until your site has been up for a while and has plenty of referrer links and other promotion, your profits aren't going to be massive, and certainly not high enough for you and your coder to spend infinite time picking at the tiny flaws in your website. If you exceed or come close to exceeding your design budget and you have a site that functions, contact your coder, pay what you owe, and call an end to the process.
But make sure to leave the door open--once you're making some money from the site, you may want to go back to that same coder in order to finally get your site to the level of perfection that you want--or to expand your site into something else altogether. Just because it doesn't make good business sense to refine your website now doesn't mean that you won't want to refine it in the future--and possibly a nearer future than you think, if your product and your overall strategy are where they should be.