Not really. Even if they give a deadline, you’re not legally bound by it if you don’t owe them anything. But just for maintaining the effectiveness of the campaign, it makes sense to respond within a reasonable time, like a week or two. In my own case, I usually responded within 2 or 3 days. In controversies like this, the one who is on the offensive usually has the advantage, so I hit right back quickly . . . to give them the strong impression that I am absolutely on top of them and We are neither wavering, unsure, wishy-washy, or lenient towards them. If you take too long, they might get the impression that you’re weak, or apathetic, and you might be easier to push over.
Your strategy is simple. One a 1:1 basis, for each thing they send you, you send one response right away. The response will always be the first dispute letter and affidavit, until and unless they get more belligerent and threatening. Then use the second letter. That’s it. It’s as simple as that. If they don’t respond point-for-point to the dispute letter and satisfy what it demands, and if they fade away from contacting you, then you have no need to pursue them any further.