When President Obama used executive orders, Republicans clamored they were unconstitutional. And indeed 12 of Obama’s actions were reversed by the the Supreme Court. I’m now being asked by my liberal friends, who slowly waking up to the fact that authoritarian government is always bad, which an executive order is unconstitutional. Here’s what I tell them:
Most important truth #1? Almost everyone is a hypocrite. The Democrats could solve world hunger and the Republicans would say it was unconstitutional. The Republicans could propose a bill be read aloud before members voted on it, and that would be opposed by the Democrats.
To get into specifics though, It depends on what an executive order covers. We have our basic separation of powers. On some issues the President is specifically empowered by the Constitution to act has he sees fit, while on others only Congress can act. When an executive order crosses that line, it becomes unconstitutional.
As an example - Libertarians were begging for President Clinton, then Bush and finally Obama to end Don't Ask, Don't Tell. Obama finally did it in 2011. This is something that was entirely in the President's bailiwick, as commander in chief. He is authorized by the Constitution to run the military, so an executive order is completely legal.
On the other hand when the President tries to do something that is a power only given to Congress, then people complain. As an example, Trump is suggesting that he will make Mexico pay for the wall by putting a 20% tax on all goods imported from Mexico. This would probably work mathematically -- the money is there. For Trump to order it however is clearly unconstitutional -- the power to tax is specifically given to the Congress.
An example of something that Obama did that was clearly Constitutional but many people claimed was not was to ban the Federal government from hiring contractors that discriminated against LGBTQ. The President is the Chief Executive of the Federal government. Hiring and firing is absolutely in his/her purview.
Political appointments are not however. As an example in 2014 President Obama made 4 political appoints to the NLRB claiming that the senate was in recess, so he did not need their consent. The Supreme Court ruled unanimously that this was an end run around the powers that are designated to Congress (advise and consent) and they declared the order unconstitutional.
Essentially every time the President issues an executive order, the question of constitutionality is "is what the President ordered something that only Congress is allowed to do." Does an executive order violate the separation of powers? A President is not a King. Neither is Congress. Each can only do what the Constitution allows. And when either oversteps their bounds the Judicial branch is charged with reversing the process.
Perhaps one of the most famous examples of this is the Line Item Veto. As you probably know, almost every state Governor has the ability to veto individual line items in a budget. The ability to selectively trim the budget helps the governor eliminate pet projects that would cost the taxpayers dearly.
In 1994 Newt Gingrich and the newly elected Republican Majority felt that the President having line item veto power was so important to balancing the budget that they used their majority to give it to Bill Clinton -- a Democratic President. There are many reasons that Bill Clinton left office with a surplus -- I think the fact that he was able to veto small wasteful pieces of the budget had a lot to do with it.
Sadly one item that he vetoed was a pork project that taxed American to give money to New York City. Even though it passed the budgeting process (thanks to powerful New York senators) Clinton vetoes it. NYC Mayor Rudy Giuliani sued saying that the line item veto violated the separation of powers because it meant the President was essentially making the budget. The Supreme Court agreed and (sadly imho) the Line Item veto went away.