It is up to the powerful majority leaders in both houses to set the legislative agenda. Committee chairmen are also chosen from the ranks of the majority party.
The current Congress will now return for a "lame-duck" session before newly-elected members take their seats in January.
One of the issues to be discussed is the extension of tax breaks introduced by George Bush, with Republicans calling on President Obama to extend them for the rich as well as the middle class.
Next year, Mr Obama will try co-ordinate with the Republican-led Congress, though he could also use his executive power more assertively if the Republicans try to block the Democratic agenda.
The president recently listed three of the areas where he might be able to work with a new Congress: reducing public spending, and immigration and education reform.
Other issues, including environmental reform, are likely to be put on hold.
What about legislation that's already been passed?
President Obama may have to fight off attempts to repeal his healthcare reform.
Republicans have promised to try to unravel the reform either by repealing sections of it or retracting financing from key provisions. They could even try to replace the reform with their own bill, but President Obama can veto this.
The Republicans have also said they want to roll back financial regulation introduced by Mr Obama in the wake of the global financial crisis.
Who was being elected?
The elections are called mid-terms because they come half-way through the four-year term served by the president, though the polls are in fact for Congress - the two houses of the US legislature - and for some state governorships (gubernatorial elections).
In Congress, all 435 members of the House of Representatives faced the voters, as they do every two years. But only about a third of the 100 seats in the Senate are up for grabs at any one time. This year, 37 Senate seats were being contested and there were 37 gubernatorial elections.
Does the president's party normally do badly in mid-terms?
The party of a sitting president often loses some seats in mid-term elections, particularly in a president's first term.
Since 1946, the average loss in a president's first term is 25 seats in the House of Representatives and three seats in the Senate. Truman (in 1946) and Clinton (in 1994) both lost 54 House seats, while Johnson (in 1966) lost 48.
Why not elect everybody at the same time?
The American system is designed to be overlapping, both in terms of the powers of the different bodies and in terms of when people are elected to them.
The House of Representatives is the larger of the two houses of Congress. It was set up as a popular body, with the number of members tied to the size of the population. The idea was for it to directly and quickly reflect the public mood, which is why the members face election every two years.
The Senate was planned as a more reflective body - senators serve for six years. Each state has two senators regardless of its size.