Is It Necessary to Apply Quickly?

It's my opinion that you need to apply for freelance writing jobs within 3 days (or less) of their posting. Now, I've entertained the thought that employers actually take time to carefully sort through the applications, giving each the time and attention it deserves, and I'm positive some do. But I've recently talked with some editors, companies and publishers that hired me, and all have stated that they received a lot of applications. When I hired my proofreader, I stopped counting (and reading) at 31 applications within the first 2 days. I made my decision on the 4th day. I simply didn't have time to keep going, and I bet many others have the same time constraints I did.

What's your time limit for applying for a freelance writing job? When will you simply not bother? 5 days? A week? Does it make a difference if it's a company versus an individual? If it's your dream job?