As befitting a republican government, the Congress established by the Constitution of the United States is invested with expansive powers. These powers are expressed in Article One of the Constitution, which is by far the longest and the most detailed in the document. Congress is given a whole host powers, including taxation, the power to regulate interstate commerce, to declare war, to print and coin money, and many others. In the context of the late eighteenth century, granting these expansive powers to the legislature was seen by many as necessary to address many of the weaknesses that plagued the country under the Articles of Confederation.
The powers of the President were considerably more limited under the Constitution. The President is Commander-in-Chief of the armed forces, has the power to appoint advisors and judges, and to conclude treaties with foreign countries. But both the appointment and the foreign relations powers were only to be carried out with the "advice and consent" of the Senate. The President also has the veto power over Congress. But overall, the powers of the President were quite deliberately limited by the Constitution.
In practice, however, the President has assumed powers well beyond those envisioned by the Framers. This has happened for several reasons. The actions of Presidents have set precedents for their successors, and over time, this has resulted in a gradual accretion of power and responsibility. For example, Presidents have, without a formal declaration of war, sent troops into many wars in many foreign conflicts. In so doing, they can point back to the actions of their predecessors who made similar decisions. Presidents have assumed extraordinary powers in response to crises, which Congress was unable to act upon with sufficient speed. Also, the President sits at the head of a bureaucracy not mentioned in the Constitution. While Congress has oversight over executive agencies, these agencies are actually tasked with carrying out government policy. Finally, Presidents have what Theodore Roosevelt, a man who dramatically expanded the powers of the office , once described as the "bully pulpit." The rise of mass media has only contributed to the reality that the President is the face of the federal government, able to influence public opinion and to take action that Congress is unable to take. These are just a few of the reasons why the President has risen in power relative to the Congress in ways not anticipated by the Constitution.
Certainly, the executive branch was the subject of Article II, from which it is not unreasonable to infer that the legislative branch, as Article I, was meant to be more important and possibly more powerful. But it is a long stretch from "important" to "supreme," and the founders really did not want to make any branch supreme. Had they wanted to do so, we could have simply had a monarchy.
In addition, we know from the existence of Article III of the Constitution and case law that the Supreme Court is meant to act as a check on congressional power. The Supreme Court of the United States is, in fact, a greater check on Congress than the executive branch is, since Congress can overrule a Presidential veto, but Congress cannot overrule the Supreme Court. If they want to try again after the Supreme Court has ruled that a statute or part of a statute is not constitutional, they can write a new law or amend one, but the Supreme Court's decision is dispositive and final as to the law that was reviewed.
Congress has passed many laws that have been held to be unconstitutional, beginning in 1803 with Marbury v. Madison. Many others have followed, including a case overturning part of the Affordable Care Act, and another overturning part of the Voters' Rights Act, all involving congressional legislation. Without the review of the Supreme Court, I am not convinced we would be a true "nation of laws," since none of us is so perfect there should not be someone looking over our shoulder, holding us to higher standards than our political needs dictate, the standards set forth by the Constitution and all of its amendments.