THINGS A PRESIDENT CANNOT DO:

• Reverse any Supreme Court decision 
• This includes Obergefell v. Hodges, which made same-sex marriage a constitutional right; Whole Woman’s Health v. Hellerstedt, which reaffirmed a woman’s right to choose first articulated in Roe v. Wade, another Supreme Court case. Grutter v. Bollinger, which instituted affirmative action, the entire body of Civil Rights case law, plus anything related to due process, including the right of minors to due process, your right to an attorney, Miranda rights, inadmissible evidence, etc.
• (Even if Trump appoints the worst possible SC nominee, they still can’t reverse any of these decisions without a really significant case coming before the Court with new facts, and then they have to write an opinion stating how this case is different than that other case…it’s unlikely to happen.)
• Write law or repeal any existing law
• While traditionally, presidents have exerted influence on the legislative agenda (see, Obama’s role in advancing and promoting the Affordable Care Act) they cannot actually write or pass legislation. Bills, joint resolutions, concurrent resolutions, and simple resolutions must be introduced in the House by a Representative.
• Presidents cannot strike down law. Only Congress can repeal laws, and only the Supreme Court can strike them down as unconstitutional.
• Presidential influence is just that—influence.
• (And if—for example—you are hated by 95% of the party you joined last week, and burned all your goddamn bridges by insulting them at various points in your campaign…..they’re unlikely to partner with you in crafting legislation.)
• Make any law or declaration that infringes in any way on the rights of the states
• So in the US, most of the rights are reserved to the states. You name it, it’s a state-run power. Criminal procedure and law? States. Medicare and Medicaid? States. The definition of marriage? States. Insurance, health departments, housing, unemployment benefits, public education, all these are state programs. And the president cannot infringe on those powers given to the states.
• (This is why down-ticket voting is so important, because Mike Pence as governor of Indiana had 800x the power he’s going to have as VP.)
• Declare war.
• This one is the most complicated, because with the advent of our “conflicts” in Vietnam, Iraq, Afghanistan, Libya, etc. there has been a significant shift in the articulation of the war doctrine, and it is one of the least restricted of the president’s “restricted” powers. But, despite all that, a president still has no power to declare war.
• Unilaterally appoint heads of administrative departments
• Unilaterally make treaties with foreign nations

Essentially, while presidents have a lot of power, it’s mostly unofficial—they can’t make sweeping laws, they can’t overturn existing rights, the most they can do is refuse to enforce them (which is absolutely a threat! and a problem! but we aren’t electing de facto royalty.