The independent voters who powered President Obama and Democrats to victory in 2008 fled to Republicans in Tuesday’s elections, helping the GOP romp to a ticketwide sweep in Virginia and a stunning victory over an incumbent Democratic governor in New Jersey.

But the night wasn’t a total loss for Democrats, as their candidate won a special election to fill an open congressional seat in upstate New York after a bitter civil war left Republicans divided between their party’s nominee and a Conservative Party candidate. The seat had been in Republican hands for more than a century.

Nevertheless, in a sign that there’s more trouble ahead for Democrats, voters in New Jersey and Virginia said they were driven by the economy and spending, and Republicans said their showing on Tuesday gives them momentum heading into the 2010 congressional elections.

Campaigning in Virginia, Republican Robert F. McDonnell said Democrats’ “overreach” in Washington helped boost him to what was a trouncing of Democratic nominee R. Creigh Deeds. And in New Jersey, Republican Chris Christie unseated the broadly unpopular Gov. Jon Corzine despite being outspent in a solidly blue state.

Mr. Christie said his election was a victory for voters “who do not want the government to fix every problem.”

“Yes, we can,” the crowd chanted, appropriating Mr. Obama’s slogan from his campaign as Mr. Christie took the stage.

Mr. Obama won New Jersey, Virginia and New York’s 23rd Congressional District in 2008, so Republicans’ showing Tuesday suggested that the red-to-blue wave that Democrats rode the past two national elections has crested. Most important, Republicans showed gains among independent and suburban voters who had defected in 2006 and 2008.

Exit polls showed independents, who made up nearly one-third of voters in both Virginia and New Jersey, went for the Republicans by a margin of nearly 2-to-1.

AP INTERACTIVE: Election 2009 results

It wasn’t just independent voters. Republicans and Democrats alike were eyeing independent and third-party candidates such as Doug Hoffman, the Conservative Party candidate in New York’s congressional race whom most Republican voters ended up backing. Meanwhile, in New Jersey independent Chris Daggett siphoned votes from the two major-party candidates.

In New York City, another independent, Mayor Michael R. Bloomberg, won his third term, though the race was unexpectedly tight. In Detroit, former basketball star and Washington native David Bing was re-elected to the mayoral post and in Boston, Thomas Menino won his fifth full term. Other big-city mayor’s slots up for grabs included Atlanta, Miami and Houston.

Voters in Maine were deciding whether to repeal a law that allows same-sex marriages, and the vote was still close Tuesday night. Meanwhile, another special congressional election in California was expected to be won by Democrats.

In Virginia’s governor’s race, Mr. McDonnell easily topped Mr. Deeds, despite the Democrat bringing moderate stances to the race and repeatedly attacking Mr. McDonnell for being too conservative in a state Democrats had touted as the ultimate “purple” state.

The entire Republican ticket ran double digits ahead of Democrats.

“For those out there who say conservatives can’t win, this rejects that notion. This is a very conservative ticket,” said Chris LaCivita, a Republican strategist who helped Virginia candidates this year and will be aiding congressional candidates in the state next year. “It’s proof-positive that solid, committed conservatives can win, and can discuss and talk about issues in a campaign that people care about. The labeling aspect just isn’t going to work.”

Mr. Obama won the New York congressional district by five percentage points in 2008, won Virginia by six percentage points and won New Jersey by 17 points.

But Democrats insisted that Tuesday’s results were neither a dress rehearsal for 2010’s congressional elections nor a referendum on Mr. Obama. They pointed to exit polls that showed 55 percent of Virginia voters and 60 percent of New Jersey voters said Mr. Obama wasn’t a factor.

Democrats pointed to history. This is the sixth time in a row that Virginia and New Jersey have elected governors of the opposite party of the president.

“The question on everyone’s mind will be: ‘What does this mean?’ The answer is simple,” said Nathan Daschle, executive director of the Democratic Governors Association. “Nothing. The party in the White House has lost these races for 24 straight years, and this election merely continued that streak. New Jersey and Virginia are independent-minded states, and tonight they reminded us of that.”

Still, Mr. McDonnell said as he campaigned Tuesday that Democrats’ “overreach” in Washington played a role in boosting him to victory.

In both states, the economy topped the list of top concerns. In Virginia health care was second, while property taxes was the runner-up in New Jersey.

In the Garden State race, Mr. Christie tried to co-opt Mr. Obama’s 2008 campaign theme of “change,” arriving at a campaign stop Monday in a black tour bus emblazoned with the message “vote for change.”

Campaigning across the state, Mr. Christie said that the race was about New Jersey and that it would be up to the White House to figure out what his victory means.

“Those people in Washington will have to figure that out,” he said.

Despite Mr. Obama’s campaigning in New Jersey, Virginia and New York and Vice President Joseph R. Biden Jr.’s making a last-minute stop in New York, the White House insisted that neither the president’s agenda nor his political prospects were on the line in those three races.

But press secretary Robert Gibbs did single out the New York congressional election as a worrying sign for Republicans. Powered by discontent with Republican nominee Dede Scozzafava, Mr. Hoffman, the Conservative Party candidate, surged in the polls, deeply splitting Republican voters in the district and forcing Mrs. Scozzafava to withdraw. She later endorsed Democrat Bill Owens.

“I think many in the Republican Party hung out a sign, as you heard people at the White House say this weekend, that moderates need not apply,” Mr. Gibbs told reporters Tuesday afternoon.

Early Wednesday morning, Mr. Hoffman conceded to Mr. Owens.

Voters in the New York district were irked they had become a national battleground, saying the issues they cared about were jobs and the local military base, not party labels. But for Republicans in particular, the race became a referendum on the direction of the party.

The Republican Party backed Mrs. Scozzafava as its nominee, but many of the party’s most recognizable leaders endorsed Mr. Hoffman, and interest groups poured money in to help him. The Club for Growth, a free-market group in Washington, said it spent more than $645,000 in radio and television advertising and its political action committee bundled another $376,000 in contributions to Mr. Hoffman’s campaign treasury.

“Hopefully, this is an unusual situation, but I think that the Republican Party hopefully will be more careful to pick somebody that has the ideas and values of a real Republican going forward,” Mr. Hoffman said Tuesday afternoon.

The seat opened up when Mr. Obama tapped Rep. John M. McHugh, a Republican, to become secretary of the Army.

The race was the latest special-election test for Republicans, who have a four-election losing streak in contested special congressional elections dating back to 2008, when they lost Illinois, Mississippi and Louisiana races. Earlier this year, they lost a close election in New York’s 20th District.

The 23rd District race also important because it was one of the last Republican-held districts in New York. Just two of the state’s other 28 seats are held by the Republican Party.

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