CBS News estimates gave Webb a narrow victory Wednesday night, but speculation swirled as to whether Sen. George Allen would seek a recount.
However, Allen is expected to concede the Virginia Senate race to Webb on Thursday afternoon, according to Republican sources quoted on the New York Times Web site.
An Allen campaign spokesman told the Richmond Times-Dispatch that no specific time has been set for Allen's announcement. However, the campaign has announced Allen will hold a 3 p.m. news conference in Alexandria, Va.
Also Thursday, Sen. Conrad Burns, R-Mont., conceded his U.S. Senate race with Democrat Jon Tester, according to the Associated Press.
The Democrats' win gives them 51 seats in the 100-seat Senate, an astonishing turnabout at the hands of voters unhappy with Republican scandal and unabated violence in Iraq.
Connecticut's Joe Lieberman and Vermont's Bernie Sanders were both elected as Independents, but will vote with Democrats.
The Senate had teetered at 50 Democrats, 49 Republicans for most of Wednesday, with Virginia hanging in the balance. Webb's victory ended Republican hopes of eking out a 50-50 split, with Vice President Dick Cheney wielding tie-breaking authority.
The sweep of Congress clears the way for Rep. Nancy Pelosi, D-Calif., to become the first female Speaker of the House and for Nevada Democrat Harry Reid to become Senate majority leader.
"This new Democratic majority has heard the voices of the American people," said Pelosi, adding that Americans placed their trust in Democrats. "We will honor that trust. We will not disappoint."
Reid said: "In Iraq and here at home, Americans have made clear they are tired of the failures of the last six years."
Pelosi and the president have had a contentious relationship prior to Tuesday's and the hope is that a lunch on Thursday will help lower the partisan temperature, reports CBS News correspondent Mark Knoller.
Mr. Bush has mocked Pelosi as "a secret admirer" of tax cuts and an opponent of measures crucial to keeping Americans safe, warning that "terrorists win and America loses" while the Democrat has characterized the president as dangerous and an "emperor with no clothes."
However, it is the president who is most likely to strike a conciliatory tone during the lunch. Mr. Bush's counselor, Dan Bartlett, quipped to the CBSEarly Show that the president's lunch menu would include, "a little bit of crow."
Speaking in the White House Rose Garden after meeting with his Cabinet Thursday, Mr. Bush called on all Republicans and Democrats to put the elections behind them and work on the issues facing the country.
Among them is Iraq, and Mr. Bush said he's "open to any idea or suggestion."
Appearing on the Early Show, Sen. Joe Biden, D-Del., told co-anchor Hannah Storm he hoped that with Democrats in control, a "political solution in Iraq" could be reached with the White House.
Biden, who will likely become chairman of the Senate Foreign Relations committee and has presidential aspirations, said, "It's up to the party and me and others to demonstrate we have a vision for where we want to take the country. It's not sufficient that we just prove we are better than the Republicans."
How much Congress and the White House cooperate depends on President Bush, Biden said. "If he really is bipartisan like he was in Texas, we get change. If he talks about it like the last four years, no," Biden said.
With power on Capitol Hill flipped, Mr. Bush faced the reality of both houses of Congress in the opposition's hands for the final two years of his presidency. He announced that, as Democrats have urged.
"I think history will mark it as the death of the Neocon movement and the beginning of a realist foreign policy that comes from both Democrats and Republicans," historian Douglas Brinkley said of the elections on The Early Show.
"The days of the Bush doctrine of pre-striking an enemy, I think, are over," Brinkley said.
In Virginia, The Associated Press contacted election officials in all 134 localities where voting occurred, obtaining updated numbers Wednesday. About half the localities said they had completed their postelection canvassing and nearly all had counted outstanding absentees. Most were expected to be finished by Friday.
The new AP count showed Webb with 1,172,538 votes and Allen with 1,165,302, a difference of 7,236. Virginia has had two statewide vote recounts in modern history, but both resulted in vote changes of no more than a few hundred votes.
An adviser to Allen, speaking on condition of anonymity because his boss had not formally decided to end the campaign, said the senator wanted to wait until most of canvassing was completed before announcing his decision.
The adviser said that Allen was disinclined to request a recount if the final vote spread was similar to that of election night.
Moving swiftly to establish himself as the winner, Webb began assembling a transition team hours after he proclaimed victory around 1:30 a.m Wednesday.
Allen's campaign, however, said the senator would wait for the completion of a full canvass — that is, a recheck of the numbers by local election officials. By law, it must be done by next Tuesday.
Lee E. Goodman, chief counsel for the Republican Party of Virginia, said the senator had not decided whether to ask for a recount.
There are no automatic recounts in Virginia, but state law allows a candidate who finishes a half-percentage point or less behind to request a recount paid for by state and local governments.
Goodman said the Republican Party was concerned about a number of glitches involving new touch-screen computer voting machines, but he said he knew of no fraud.
The State Board of Elections is set to meet on Nov. 27 to certify the results. Allen would have 10 days after that to ask for a recount, which would be overseen by three judges.
In an all-around banner election year for Democrats, voters frustrated about the direction of the country toppled Republicans at all levels of government in a searing rebuke of the status quo.
"It was a thumpin'" Mr. Bush told reporters at a White House news conference. "It's clear the Democrat Party had a good night."
The president, who spoke of spending his political capital after his re-election triumph two years ago, acknowledged, "As the head of the Republican Party, I share a large part of the responsibility."
The war in Iraq, scandals in Congress and declining support for Mr. Bush and Republicans on Capitol Hill defined the battle for House and Senate control, with the public embracing the Democrats' call for change to end a decade of one-party rule in Washington.
With the GOP booted from power after a 12-year House reign, lame-duck Speaker Dennis Hastert, R-Ill., announced he will not run for leader of House Republicans when Democrats take control in January.
Connecticut Sen. Joe Lieberman, according to CBS News correspondent Gloria Borger stands to gain power within the Senate, despite losing the Democratic primary in his re-election campaign. "If the congressional centrists are looking for a leader, it might be Joe Lieberman. The newly Independent senator could be courted by both Republicans and Democrats looking for votes," Borger said.
In the House, Democrats won 230 seats, putting them on track for a 30-seat gain if trends held in remaining unsettled races, CBS News estimates.
Aside from gains in Congress,to give them a majority of top state jobs — 28 — for the first time in a dozen years. New York, Ohio, Massachusetts, Colorado, Maryland and Arkansas went into the Democratic column.
In down-ballot races, Democrats gained a decisive edge in state legislatures, taking control of a number of bodies and solidifying their hold on others. With the wins, Democrats will be in a better position to shape state policy agendas and will play a key role in drawing Congressional districts.
According to CBS News exit polls: