The American Republic will endure until the day Congress discovers that it can bribe the public with the public's money. Alexis de Tocqueville
In a book ---Washington, A Life--- the author writes about the debate by the Constitution Convention on the subject of the executive branch. Delegates had difficulty conceiving a strong presidency that did not look suspiciously like a monarchy. The idea of a separate executive branch with a president independent of the legislature and able to veto its laws was regarded as heretical, in some quarters. Benjamin Franklin pushed for a small executive council instead of a president. When you look at the constitution remember that discussions of the executive branch assumed George Washington was going to be the first president and therefore benevolent. His successors were feared.
GW voted for requiring a three-fourths majority in Congress to override a presidential veto. The convention was not as concerned so it approved a two-thirds majority to forestall executive powers. You may rue that day.
US presidents have issued executive orders since 1789, GW being president. Although there is no Constitutional provision or statute that explicitly permits executive orders, there is a vague grant of "executive power" given in Article II, Section 1, Clause 1 of the Constitution, and furthered by the declaration "take Care that the Laws be faithfully executed" made in Article II, Section 3, Clause 5. Most Executive Orders use these Constitutional reasonings as the authorization allowing for their issuance to be justified as part of the President's sworn duties, the intent being to help direct officers of the US Executive carry out their delegated duties as well as the normal operations of the federal government: the consequence of failing to comply possibly being the removal from office.
If Congress does not like what the executive branch is doing, it has two main options. It may rewrite or amend a previous law, or spell it out in greater detail how the Executive Branch must act. The President has the right to veto the bill if he disagrees with it, so, in practice; a two-thirds majority is often required to override an Executive Order.
In addition to congressional recourse, Executive Orders can be challenged in court, usually on the grounds that the Order deviates from "congressional intent" or exceeds the President's constitutional powers.
As I have often said the president is not the problem, Congress is the problem. The president can do nothing with which two thirds of congress and/or court does not agree.
Congress: Bingo with billions. --- Red Skelton