"This is a very troubling attempt to stifle the free speech of Americans who have the constitutional right to express their opinion and concerns about health care," said Jay Sekulow, chief counsel of the American Center for Law and Justice. He called on Obama to repudiate his blog.
"This move is an attempt to intimidate those who have legitimate concerns about the health care plan," Sekulow said. "And, worse, it turns the White House into some sort of self-appointed 'speech police.' This new White House reporting program strikes at the heart of the First Amendment and has no place in this important debate about health care."
Sekulow said he imagines that opponents of mandatory abortion coverage are engaging in what the White House considers "fishy" speech and should be reported.
"What the White House is touting is absurd," he said.
But Napolitano said the White House probably cannot be sued because of sovereign immunity, unless someone was harmed by what the government did with the records. But that's unlikely, he said, because the person would probably be unaware of the harm.
"That's a silent violation of your right to privacy," he said.
The ACLU said in a statement to FOXNews.com that the White House blog is a "bad idea that could send a troublesome message."
But the organization added, "While it is unclear at this point what the government is doing with the information it is collecting, critics of the administration's health care proposal should not fear that their names will end up in some government database that could be used to chill their right to free speech."
The White House Thursday denied that it was playing "Big Brother."
"Nobody is collecting names," White House spokesman Robert Gibbs said. "We have seen, and as I've discussed from this podium, a lot of misinformation around health care reform, a lot of it spread, I think, purposefully."
Texas Sen. John Cornyn, who has called on Obama to end the program, rejected the White House explanation.
"Of course the White House is collecting names," he said, arguing that anyone with access to the e-mail account has access to private information.
"The question is not what the White House is doing, but how and why," he said. "How are they purging names and e-mail addresses from this account to protect privacy? Why do they need the forwarded e-mails, names, and 'casual conversations' sent to them instead of just the arguments that they want to rebut?
Asked by FOX News whether the White House was using the blog post as a way to expand the e-mail list for the administration and Obama's political arm, Organizing for America, Gibbs said the two are "not in any way connected" and repeated that the White House is not collecting names.
Pressed about the program's goal, Gibbs said it was to clarify for everybody what the misinformation is, adding that's not a new tactic.
"When you make a mistake in your report, sometimes I e-mail you," Gibbs said to FOX News' Major Garrett. "Occasionally, I call. Sometimes I just throw something against the wall. Occasionally, it's all three."
Garrett asked why it's necessary to ask so many people to e-mail the White House.
"All we're asking people to do is, if they're confused about what health care reform is going to mean to them, we're happy to help clear that up for them. Nobody's keeping anybody's names. I do have your e-mail. ...Maybe that's because I assume future mistakes. But I'm not going to say that," Gibbs said, drawing laughter.
"But nobody's collecting information," he added. "Everybody is trying to give people only the facts around what we all understand is a very complicated issue."