Projections by television networks showed Democrats gaining at least 10 Republican seats in the house of representatives, putting them two-thirds of the way to picking up the 15 they need for a majority.
NBC, a US TV station, has forecast that the Democrats will win control of the House of Representatives.
The Democrats are also projected to take key three seats in the Senate.
A Democrat majority in even one chamber of Congress would reduce Bush’s influence, block his legislative agenda and turn up the pressure on the White House for a shift of direction on Iraq.
Rick Santorum, a conservative once considered a rising star of the Republican party, was beaten in Pennsylvania, US television networks reported.
And in Ohio, the Democrats beat Republican incumbent Senator Mike DeWine, networks said.
The Democrats also scored an early victory in the battle for Congress, with Brad Ellsworth defeating Republican John Hostettler in Indiana.
Hillary Clinton retained her New York senate seat, and Joe Lieberman, who lost the Democratic nomination in Connecticut won as an independent candidate.
Opinion polls suggest that increasing dissatisfaction with George Bush’s policies, particularly over Iraq, means that the Democrats’ optimism is likely to be rewarded when results are announced on Wednesday.
Health care costs
Much of the result will also hinge on how much issues such as health care costs, “values” issues such as stem-cell research, gay marriage and abortion, the economy and illegal immigration, weigh on voters’ minds.
As millions of people turned out to vote, problems were reported with electronic voting machines in eight states.
Lieberman won in Connecticut
In Virginia, election officials have asked the FBI to investigate allegations of voter intimidation.
Early exit polls from the ABC television network showed that six in 10 voters disapprove with the way Bush was doing his job.
CBS exit polls found 57 per cent of voters asked disapproved of the war in Iraq, which has claimed the lives of more than 2,800 US soldiers.
During the last full day of campaigning on Monday, both parties began get-out-the-vote operations designed to bring core supporters to the polls.
Bush, hampered by low approval ratings and confined to appearances in Republican areas to avoid alienating independents, was snubbed on Monday by the Republican candidate for governor in Florida, who did not appear with the president at a rally.
None the less, the US president exhorted his party members to make their presence felt at the polls.
Former president Bill Clinton
“I knew we were going to finish strong,” Bush said during a final campaign rally in Pensacola, Florida, on Monday evening.
“Republicans are going to turn out and it’s going to be a great victory.”
The Democrats have savaged Bush over Iraq, saying he and Republicans are in denial as US troops continue to die and chaos envelops the country.
“It has become clearer than ever that our current course in Iraq is unsustainable,” said Wesley Clark, a former Democratic presidential candidate and US general, urging Democrats to “stand up and be counted”.
Howard Dean, chairman of the Democratic National Committee, urged his party members to cast their votes.
“We offer a fresh start and a new direction, but each and every Democrat must get to the polls to make our vision a reality,” he said.
Democrats could recapture the US House of Representatives for the first time since 1994, with control of the upper house, the Senate, turning on several races that are too close to call.
All 435 House seats, 33 Senate seats and 36 governorships are at stake. Democrats need to pick up 15 House seats and six Senate seats to gain control of both houses.