While no one is expecting a repeat of the 36-day standoff witnessed in the 2000 presidential election, many races may not be settled on Nov. 6, the day after voters go to the polls to select the entire House of Representatives as well as senators and governors in a third of the states.
In Louisiana, the Senate candidate must win at least 50 percent of the vote to avoid a run-off in December. Incumbent Democratic Sen. Mary Landrieu is polling well ahead of eight other challengers, but she is not polling at 50 percent. Ten percent of voters, though, are still undecided.
In Hawaii, if incumbent Democratic Rep. Patsy Mink is elected, voters will have to go back to the polls for a special election. Mink, 74, died in late September of viral pneumonia, but it was too late to take her name off of the ballot. The special election will be held Jan. 4, right before the start of the new congressional session.
In the meantime, another special election will be held Nov. 30 to fill out her existing term, which expires in January. Mink's widower has said he will run for that slot, though he will not run for a full term.
And even with winners in place, Congress could have a shake-up or two before the next session begins.
In Alaska, Sen. Frank Murkowski is running for governor. If he wins, he will have to quit the Senate and appoint his own replacement.
In Missouri, Sen. Jean Carnahan was appointed to her seat two years ago when her husband posthumously won the 2000 election. But if her opponent -- former GOP Rep. Jim Talent -- wins, according to Missouri law, he is to be sworn in immediately to complete the remaining four years of the six-year term.
That could tilt the majority of the Senate to Republicans for the remainder of the term. After Sen. Paul Wellstone's death last week, each party has 49 members. Independent Vermont Sen. Jim Jeffords votes with Democrats. If Talent makes the Senate an even 50-50, Vice President Dick Cheney would be the deciding vote.
But before Talent can join the Senate, his election must be certified by Missouri's Democratic Gov. Bob Holden, who defeated Talent in the 2000 governor's race.
"The law is so vague that it may allow Holden to delay," said Saint Louis University political science professor Kenneth Warren.
However, Spence Jackson, spokesman for Missouri's secretary of state, a Republican, said, "I think the pressure coming from the general public, from all Missouri voters regardless of party, would be very, very intense" for Holden to quickly sign certification.
But there is a major catch to the Republican hope. Even if Talent wins and the Republicans take the majority, it may only last through Dec. 2 if Murkowski wins his gubernatorial race in Alaska.
In that case, Murkowski will resign from the Senate at noon on Dec. 2, leaving his seat vacant. Alaska succession law requires at least five days between a senator's resignation and the governor appointing his replacement, said Bob King, spokesman for term-limited Democratic Gov. Tony Knowles.
King said the law was passed "just purely to allow Frank Murkowski to pick his own successor should he be elected governor."
Democrats would then have control of the Senate again, assuming the other races remain even.
Another event could also leave Congress' electoral composition up in the air.
If convicted former Ohio Rep. James Traficant were to actually win re-election from his prison cell in Pennsylvania, he would be the first to serve from a jail cell in 200 years, following up on Matthew Lyon of Vermont.
Traficant, who was sentenced to eight years in prison for bribery and racketeering, was tossed out of the Congress by his colleagues after his conviction. If he were elected -- and he knows at least one less vote is coming his way since he is barred from voting -- the next Congress could expel him again, leaving Ohio's 17th congressional seat vacant.
The Associated Press contributed to this report.