Senator Cornyn Asks Why
Americans are being asked to turn in their fellow citizens for exercising their First Amendment rights?

I am not aware of any precedent for a President asking American citizens to report their fellow citizens to the White House for pure political speech that is deemed "fishy" or otherwise inimical to the White House's political interests.
By requesting that citizens send "fishy" emails to the White House, it is inevitable that the names, email addresses, IP addresses, and private speech of U.S. citizens will be reported to the White House. You should not be surprised that these actions taken by your White House staff raise the specter of a data collection program. As Congress debates health care reform and other critical policy matters, citizen engagement must not be chilled by fear of government monitoring the exercise of free speech rights.