Final answer:
Running for a third term as President of the United States would be unconstitutional, as the 22nd Amendment to the Constitution limits the office to two terms. Presidents have gained more tools of power over time, yet the term limit remains firmly entrenched and cannot be sidestepped without a constitutional amendment.
Step-by-step explanation:
In the scenario provided, where the President decides to run for a third term in office due to terrorist threats against the United States, such an action would be unconstitutional. This is because the 22nd Amendment to the U.S. Constitution explicitly limits the presidency to two terms. This amendment was ratified following Franklin D. Roosevelt's four-term presidency, with the aim of preventing any future president from serving more than two terms and thus preserving the balance of power among the branches of government.
Despite the fact that the presidency has evolved and expanded in power over time through tools like executive privilege and executive orders, and even though emergencies may create opportunities for stronger executive action, a third term would require a constitutional amendment or an extraordinary situation not currently accounted for in law. Congress also has mechanisms in place, such as amending the Constitution, to check presidential powers. In light of these provisions, no matter the external circumstances such as terrorist threats or wartime, a president cannot override the Constitutional two-term limit single-handedly.