Which of the three sources of law has the strongest impact on the U.S. healthcare system?

The three sources of law correspond with the three co-equal branches of U.S. government (legislative, executive, and judicial), which exist both on the federal level and within each of the states. Before we get there, a little background: the U.S. Constitution is the supreme law of the land. 

The U.S. Constitution creates the three branches of our government, grants them specific powers, and by way of the Amendments enumerates various constitutional rights. The U.S. Constitution...

The three sources of law correspond with the three co-equal branches of U.S. government (legislative, executive, and judicial), which exist both on the federal level and within each of the states. Before we get there, a little background: the U.S. Constitution is the supreme law of the land. 

The U.S. Constitution creates the three branches of our government, grants them specific powers, and by way of the Amendments enumerates various constitutional rights. The U.S. Constitution derives its power from the states, which each have their own constitutions that follow a similar structure. Under the 10th Amendment, any powers not specifically given to the federal government are reserved to the states. The U.S. Constitution is the ultimate source of law nationwide, and each state constitution is the ultimate source of law within that particular state. After constitutional sources of law, we look to the three branches of government, which each have lawmaking powers in their own right.

The legislative branch of government literally has the power to create new laws in the form of legislation/statutes. On the federal side this power is vested in Congress, consisting of both the House and the Senate, and is limited to what is stated in Article 1, Section 8 of the U.S. Constitution. The specific power relevant to U.S. healthcare would be the commerce among the several states. On the state side, the state legislatures have broad powers to enact any law consistent with federal law and the state constitution. This means that states have the ability to enact more comprehensive healthcare laws than the federal government, according to the needs of the people of that state. The Affordable Care Act (ObamaCare) is the current cornerstone of federal healthcare law.

The executive branch of government has the power to enforce and implement the law. On the federal side, this power is vested in the president, who oversees the various executive and administrative agencies under that office, including law enforcement. On the state side, it is vested in the governor, who is the head of the executive branch of the state and the various agencies therein. The executive power to enforce the law comes with it the power of enforcement discretion—that is, the ability to prioritize which laws will be enforced, and to determine how they will be enforced. Healthcare law is enforced by various federal executive agencies, such as Health and Human Services. 

The judicial branch of government has the power to interpret the law and say what the law means. On the federal side, this power is vested ultimately in the Supreme Court, which is the final authority as to what the U.S. Constitution and federal laws mean, and also has the power to invalidate state laws that are inconsistent with federal law. Each state also has a Supreme Court (though not always called that) which is the final authority as to what the state constitution and state laws mean. Courts hear cases and controversies and issue judicial opinions, which affect how future cases are decided. Health care law cases are part of these.