All 435 seats in the House of Representatives and about one-third of the 100 Senate seats are at stake in the elections.
In both chambers, Republicans now control slim majorities.
In the House, Democrats need to gain 12 seats to win control of the chamber.
That number increased by one in August after Louisiana Congressman Rodney Alexander switched his party affiliation from Democrat to Republican in his re-election bid.
Some Democrats believe they have a chance of winning back the majority they lost in 1994. Their hope stems from public opinion polls showing many Americans are concerned about the direction the country is taking with the respect to the war in Iraq and the economy.
But many political observers are not so sure about the Democrats' prospects. They note there are only a few competitive races. They also say incumbents in the House are generally re-elected.
The Cook Political Report, an independent nonpartisan newsletter, says for the past 10 election cycles, the re-election rate for House incumbents has been 95 percent or better.
In the Senate, Republicans have a razor-thin majority: effectively just one seat in a chamber of 51 Republicans, 48 Democrats and one independent, Senator Jim Jeffords of Vermont, who usually votes with the Democrats.
Democrats will need to gain two seats to win control in the Senate if President Bush is re-elected. If Democratic presidential challenger John Kerry is elected, Democrats would need a gain of just one seat. That would allow John Edwards, who would become vice president, to cast any tie-breaking votes.
The head of the Democratic Senatorial Campaign Committee, Senator Jon Corzine of New Jersey, says his party has a field of strong candidates that could win a 51-seat majority or better in the Senate.
"Does this mean we are going to get to 51?" he asked. "I would not be surprised if we did. We are in a good position to make that happen, maybe even exceed that number."
But doing so will not be easy. Many of the closest Senate contests are in states where President Bush, the Republican Party's nominee for the White House, is very popular.
Republicans are optimistic they will retain their majority. The head of the Republican Senatorial Campaign Committee is Senator George Allen of Virginia.
"I am confident, ladies and gentlemen, that the Republicans will strengthen the majority in the United States Senate in elections this fall," he noted.
Of the nine Senate seats that are most competitive, three are held by incumbents, including Alaska Republican Senator Lisa Murkowski, Kentucky Republican Senator Jim Bunning, and South Dakota Democratic Senator Tom Daschle, who serves as his party's leader in the Senate.
Mr. Daschle's race against Republican challenger John Thune, a former South Dakota Congressman, is perhaps the most closely-watched of all the Senate races.
In a state that Mr. Bush won by 22 percentage points four years ago and where he remains popular, Senator Daschle is running television advertisements showing him hugging the president, with whom he is usually politically at odds.
Mr. Thune criticized the ad as a cynical attempt by Mr. Daschle to connect himself with a popular president.
Mr. Daschle says he embraced the president after Mr. Bush addressed a joint session of Congress in the wake of the September 11, 2001 attacks. He says the ad shows that politicians can work together in times of crisis.
But the South Dakota race has been anything but conciliatory.
Mr. Thune has taken aim at Mr. Daschle's criticism of Mr. Bush's handling of the war on terror and the war in Iraq.
"What it does is embolden our enemies and undermines the morale of our troops," he said.
Mr. Thune spoke on a recent "Meet the Press" program on NBC, as did Mr. Daschle, who responded:
"He knows that is wrong," said Mr. Daschle. "His effort to demonize me will not work in South Dakota."
The other states with competitive Senate races include Oklahoma, Colorado, Florida, Louisiana, and North and South Carolina.
