Not a bad idea I suppose, we have something similar here (Britain) which seems a little more useful, I think parliment has to "debate" the issue rather than someone just "responding" to it. Either way, they don't actually have to do anything about it but I'm not against the idea.
I think it's a good way for people who aren't necessarily the most vocal to express their concerns. For example, I wouldn't actually go and protest or petition in public for very much, but I've already voted for a bunch of things I strongly agree with and made a petition.
I feel like the middle of the road Americans tend to not be represented just because they're the least likely to have a big public outcry or do anything severe about it. This seems like a good way for them to show what they actually support rather than politicians having to gauge off the 500 people who just happen to be angry enough to stand outside their door.