The electoral pattern was set in the U.S. Constitution with the objective of creating a representative but not necessarily united government. The principles of checks and balances were originally primarily confined to the legislature, as defined in Article I of the constitution, and the executive as defined in Article II. Unity of government was not something that the founders thought was a good thing, because it would allow one faction to dominate the country, and so the structure of the U.S. government was set up to make unity difficult, without massive popular support.
The legislature enacts laws, passes budgets and serves as the primary check on the executives power. The lower house, the House of Representatives, is intended to represent the "masses" and is elected every two years. The biennial elections force the House to be more responsive to the people. The upper house, the Senate, was originally elected by the state legislatures and was intended to represent the governments of states. With the passage of the 17th amendment the Senate became elected directly by the people, but each Senator serves a term of 6 years, and are elected in three roughly equal classes. The longer terms allow Senators to be be more "deliberative" and take a longer view of issues.
The President, as the executive, was the power that the Founding Fathers most feared, and was the power the legislative branch was intended to balance against. The president being elected every four years meant that he would be at a relative disadvantage to the Senate, in terms of strategic planning, and be constantly subject to change in the House because of people's dissatisfaction.
This system was set up to strike a balance between stability, which could lead to domination and tyranny, and chaos, which would leave the country ungovernable. While there was a chance that the government could be united with a single faction controlling the Senate, the House and the Presidency, that was not the objective. It was feared that unified government would lead to tyranny. Therefore the difficulty in creating a unified government is actually a feature and not a bug.
It stands in stark contrast with the parliamentary system, which always has a unified executive and legislature, because the executive is drawn from the legislature, in the form of the Prime Minister, which means that the party in power can always enact their policies more or less as intended. On the other hand, Parliamentary systems are reliant upon the ability to call frequent, short elections, in order to remain representative, and at times that has led to extended periods of instability, with frequent governmental collapse.
The contrast between the two can be illustrated with the metaphor of two ships of state. One, the presidential system, moves slowly and turns slowly, but is consequently fairly consistent in its movement. The other, the parliamentary system, can turn on a dime, but may dart back and forth and even completely reverse direction, sometimes abandoning its advances completely.