Rest assured, First Amendment lovers, that a hypothetical President Trump could not unilaterally change the libel laws. A big reason why President Obama's executive actions on immigration and gun control are so controversial is because they raise questions about whether he reached beyond the limits of presidential power. It's hard to imagine any serious debate about an attempt to alter libel laws, however; such an effort would clearly exceed Trump's — or any president's — authority.
Alternatively, Trump could simply use the bully pulpit to promote a culture of frivolous libel suits that ultimately wouldn't go anywhere but would force media companies to spend precious resources on defending themselves. If his goal is to cause news outlets to lose money, Trump could conceivably achieve that objective without changing any laws at all.
But if he really wants to lower the bar for legitimate libel claims, he does have one recourse — a rather topical one, actually, in the wake of Supreme Court Justice Antonin Scalia's death. Through judicial appointments, Trump could theoretically reverse decades of legal precedent that requires a public figure like him to prove "actual malice" in a libel case.
To win a defamation case, a plaintiff must show four things: 1) a false statement purporting to be fact; 2) publication or communication of that statement to a third person; 3) fault; and 4) damages, or some harm caused to the person or entity who is the subject of the statement.
Since the U.S. Supreme Court's 1964 decision in New York Times v. Sullivan, defamation claims have been limited by First Amendment concerns. Thus, for instance, public officials and public figures (people who are famous) must show that statements were made with actual malice to recover in an action for defamation. Actual malice means that a statement was made with knowledge that it was false or with reckless disregard of whether or not it was false. In addition, a plaintiff must show actual malice by "clear and convincing" evidence rather than the usual burden of proof in a civil case, preponderance of the evidence.
A private person suing about a matter of private concern need only show negligence, meaning that the defendant knew the statement was false, or would have known if she or he had exercised reasonable care.
The key here is that the "actual malice" standard for public figures is not codified in federal law; it is merely a longstanding legal precedent.
Precedents can change in the hands of the right (or wrong, depending on your perspective) judges. In one notable recent example, the Supreme Court's 2010 Citizens United decision reversed at least 20 years of legal precedent on corporate spending in politics.
Trump, of course, would need congressional approval of his judicial nominees. And he would need just the right case to work its way up to the Supreme Court and for a majority of the justices — most of whom would not be his appointees — to overturn Times v. Sullivan. This is a pretty far-fetched scenario.
But it is technically possible, without Congress acting on a new law, to lower the libel standard for public figures to match the one applied to private citizens. That would accomplish Trump's mission to make it easier for people like him to successfully sue media companies.