The executive branch of the U.S. government is massive because it includes all of the agencies that are responsible for enforcing federal law or executing the functions of government. The agencies that "enforce the law" include all of those who work in federal law enforcement, from the Department of Justice (DOJ) to Immigration and Customs Enforcement (ICE) to the Federal Bureau of Investigation (FBI). The agencies that perform the "functions of the government," on the other hand, include national security interests and the armed forces. There are also many other federal agencies that are included in the executive branch that perform national interests, as well, including the National Aeronautics and Space Administration (NASA) and even the Post Office. These also employ thousands of people, each.

As a result, the executive branch employs more than 4 million Americans.

The Executive Branch can be broadly defined as the part of the Federal Government that enforces laws.

This question actually provides an excellent exercise in exploring not only the scope and responsibilities of the Executive Branch in particular, but also the two-million-person-strong workforce of the Federal Government as a whole.

While many think of the Executive Branch as the President, the Vice President, the Cabinet, and their staff, this is only a drop in an ocean. A good place to begin an exploration into anything having to do with employment is the Bureau of Labor Statistics (BLS).

The small snippet of information on that BLS page outlines the Executive Branch as consisting of the President, the VP, the Cabinet, and the fifteen Executive Departments (Defense, Labor, Homeland Security, Education, State, etc.), independent agencies such as the EPA, and even the Smithsonian Institute. In addition, many Federal Agencies such as the Census Bureau and the CDC operate under the aegis of one of the fifteen Executive Departments.

If one counted each worker in all of these departments, which the government does, the figure would be around two million workers for the fiscal year 2015. The precise number, and breakdown of the type of work, can be found on the website of the Office of Personnel Management.