Although George Washington advised in his Farewell Address that the United States stay out of European affairs, this became impossible during Adams's one-term presidency, which began in 1797 and ended in 1801. He was forced into the morass of the growing tensions for control of the seas between Britain and France. A chief problem was that American merchants who shipped their goods to Europe across the Atlantic were increasingly subjected to search and seizure by both British and French vessels. A scandal erupted, too, when the French government, starved for cash, demanded payments from the United States to come to the negotiating table to try to work out problems.

Because of worries that the United States might be attacked by Britain or France, Adams was forced to increase national security and enlarge both the army and the navy. This led to higher taxes, which led to unrest. In Pennsylvania, John Fries, for example, organized a tax revolt and a militia to go after the tax assessors who were increasing taxes on farmers. At the same time, Adams supported the passage of the highly unpopular Alien and Sedition Act, which curtailed free speech and freedom of the press, as well as making it more difficult for immigrants to become US citizens.

In a nutshell, the shocks of growing warfare in Europe spilled over into the United States, leading to unpopular taxes and limits on freedom that doomed Adams's reelection chances.

By the time that John Adams became President of the United States, relations between America and its former ally France were at a low ebb. This was largely a consequence of the United States having signed the Jay Treaty with Great Britain in 1795, which the French perceived as a hostile act.

Ever since then, the United States had been in a state of quasi-war with France. In other words, the two nations were hostile towards each other without actually engaging in armed conflict. Adams knew that the very last thing that the United States needed was another war so soon after the Revolutionary War. So he was placed in the difficult position of having to avoid an outright conflict with France while at the same time saving face.

But this was easier said than done. The French were becoming more and more aggressive, attacking American ships that traded with Great Britain. To counter this growing threat to transatlantic trade, Adams adopted a two-pronged approach. On the one hand, he sought a diplomatic solution to the crisis. On the other, he called for a military buildup that would enable the United States to defend itself against French hostility.

In the event, Adams was able to secure a diplomatic resolution to the crisis. But this came too late to save Adams's presidency. Adams had made himself spectacularly unpopular due to his signing of the hugely controversial Alien and Sedition Acts, which represented a serious attack upon the rights and civil liberties of the American people.

One of the main problems Adams faced during his presidency was the Quasi-War with France (1798-1800). While most Americans were pro-French in the ongoing power struggle between France and Britain, Adams was alarmed by the French seizure of American merchant ships. The French believed that the United States was in support of Great Britain. However, most Americans still supported the French (as the French had supported the American Revolution) until the so-called XYZ Affair of 1797 in which three American envoys to Talleyrand's government in Revolutionary France were asked to pay a large bribe before they could negotiate. After that incident, popular sentiment in the United States turned against France.

Adams attempted to build up the army and navy in defense of the threat he felt France posed, and, to do so, he instituted a tax in 1798 that was highly unpopular and that sparked rebellions in rural Pennsylvania. He also passed the highly unpopular Alien and Sedition Acts of 1798, which made it illegal to publish "malicious writing" against the government and that imposed fines and prison sentences for doing so. The acts also lengthened the time it took for immigrants to become citizens. Whether or not these acts were widely used is still debated among historians, but the unpopularity of the acts helped lead to Jefferson's election from the Democratic-Republican party in 1800.

John Adams faced several problems while he was president. For the first time, we had political parties in an election. Thus, while Adams won, he had political opposition. In fact, his Vice President, Thomas Jefferson, was from the political party opposed to Adam’s political party. Adams represented the Federalist Party while Jefferson represented the Democratic-Republican Party.

We had issues with France. The French were seizing our ships and interfering with our right to trade. When we sent representatives to France to discuss this, the French wouldn’t meet with them for several weeks. When they eventually met our representatives, they demanded a loan and a bribe. Americans were outraged at this treatment, in what became known as the XYZ Affair. They wanted Adams to go to war. Adams knew going to war was not in our best interests, so even though it hurt him politically, he used diplomacy to end the crisis.

At home, the passage of the Alien and Sedition Acts hurt President Adams. The Sedition Act made it illegal to criticize the government. That conflicted with our right to free speech. The Alien Act made it harder for an immigrant to become a citizen by lengthening the waiting period from five to fourteen years before a foreigner could become a citizen. It also made it easier to deport an immigrant. The Alien Act was clearly aimed at hurting the Democratic-Republican Party since many immigrants were joining that party. The passage of this law helped to make Adams and his party unpopular.

Partially as a result of the growing unhappiness with President Adams and the Federalists, the Democratic-Republicans won the election of 1800.

What problems plagued John Adams in his one term as president?

One of the most significant problems that plagued John Adams in his term as President was his inability to bring people together.  Adams faced challenges both from within his own party and outside it.  Effectively placing him on an island, this plagued him and limited him to one term.

Adams was never quite comfortable with political labels and factionalization.  Yet, within the post- Washington political discourse, this was the reality into which he entered.  Adams was not comfortable with the Jeffersonian Democratic- Republican model of leadership.  Yet, Adams held more discomfort within the membership of his own party.  His division with Alexander Hamilton, the embodiment of the Federalist brand, impacted his leadership capacity.  Adams found himself fending off the Hamiltonian Federalist partisans as well as the Jeffersonian Republicans.  This put him in isolation when the election of 1800 emerged.  For Adams, the inability to bring people together plagued him throughout his Presidency and proved to be a hurdle that could not be overcome.