I don't think this is something to worry about.
Note that I'm very paranoid about civlib stuff and suppression of dissent. I have some family history with authoritarian regimes so it means a lot to me. And I am watching Obama closely because I think he's often tempted to step over the line. (Habeas corpus, anyone? Or, what about the army of volunteers -- nice folks, but still -- promoting the President's agenda across the country? I talked to some of them and asked what they did, and it was all, "We support the President and tell people about his policies" and they had no idea that there was a propagandistic aspect to that.)
But back to this. They're not asking for the names of opponents of health reform. They're asking to see rumors -- stuff published on websites or chain e-mails, stuff that is either public or soon to become public. The administration has had problems with terrifying rumors gaining traction (and yes, a lot of them are false. "Obama is foreign-born." "Obama is a Muslim." "The health care plan includes euthanasia of the elderly.") So now they want to nip them in the bud before they take on a life of their own. I'd be worried if they were taking the names of dissenters, but they're just asking for links.
Why can't they do that themselves? Well, they'd have to pay some college grad who'd probably surf the web at work. Why do that when regular citizens will do it for free? It's called crowdsourcing and it works.
(And by the way, Pat, I sincerely hope you never have trouble with the government. I don't think it's likely, but if I'm wrong, I think you have people here who will try to help. Sometimes I worry that the day will come in my lifetime when dissent will be dangerous in America.)