The Founders gave a lot of thought and debate to safeguarding individual rights. They knew well the violent history of the oppressive European monarchies, including their own ancestral homeland of England. They understood the risks of unbridled power in the hands of unaccountable heads of state.
The Federalists, led by Alexander Hamilton, John Adams, and John Jay, seemed confident that a strong central government would rule humanely. But the Anti-Federalists, led by Thomas Jefferson, John Adams, and Patrick Henry, had their doubts. Indeed, they first opposed the new constitution entirely, because they saw it as shifting too much power from the states and local communities to a central government.
The Anti-Federalists blocked the new constitution until the Federalists agreed to add specific amendments that would guarantee individual rights and limit the powers of the central government. Once they made that deal, both sides agreed to approve the constitution in 1788 to get the new Republic started. They went ahead with the understanding that immediately thereafter they would add a series of amendments that would finish the job.
Both sides kept their word. Shortly after ratification the new Congress, created by the new Constitution, adopted the first ten amendments that have become the legendary American Bill of Rights.
By the way, when it comes to amending the Constitution, you might like to know that the President has no role in the process. Under Article II, he or she has no authority to initiate, approve, or veto a constitutional amendment.