This article is not quite as USA-centrist but describes world history events where public opinion had a huge influence on policy being made. One US example is Pearl Harbor, which turned the anti-war sentiments into the urge for revenge. This is a limit because sometimes the president must decide how important public opinion is to them to make decisions, and whether it is best to give in to public pressure or not.
This article describes how the Constitution limits the Executive Branch with Congress, and how many presidents have complained about their laws not getting passed and blamed it on the Constitution. But getting rid of all of the other branches would give them too much power, which is certainly worse than not having a few laws passed. This is definitely an example of a limit on the Executive Branch.
This article talks about Trump's visit to the Middle East and meeting different country leaders. This article might have a bit of bias, saying that the visit did not clarify any foreign policy but was just a visit. How the policy may change is ambiguous at the moment, despite the visit, is the conclusion of the article. This is a power of Chief Diplomat, deciding how our country is represented to others'.
This article talks about how the President can be a party leader, and cites Reagan as the best example of a party leader for the Republican Party. It talks about how he sacrificed some of his popularity for certain beliefs and helped the party grow tighter as an identity and a group. This is showing the power of a President being the party leader and having a strong effect on thousands of people.