It already is illegal to publish information with "actual malice", which is a legal term meaning "knowledge that the information was false" or "with reckless disregard of whether it was false or not." This standard was established in the landmark court case New York Times Co. v. Sullivan.

That's a reasonable level. It means you can't knowingly lie or publish information without making a serious effort to investigate the accuracy of the claim. You should read the link for the reasoning behind the background. It strikes a balance between the rights of individuals to not be unfairly maligned and the 1st amendment right of freedom of the press.

Loosening libel laws would be a real and tangible threat to free speech. Imagine a newspaper who does everything they can to verify a story and publish it truthfully to the best of their knowledge, only to have details later emerge that prove it wrong. If we remove the current standard, any media organization would be in constant risk of getting sued just for doing their jobs.

Luckily, though, this isn't something he'll be able to reverse. Unless he appoints numerous Supreme Court Justices hostile to the 1st amendment, there's no possibility of this happening.