By Steve Holland

WASHINGTON (Reuters) - Republicans seeking a comeback from recent losses may pick up the governors' seats in Virginia and New Jersey on Tuesday in campaigns that tested the limits of U.S. President Barack Obama's influence.

Early returns in Virginia gave Republican Bob McDonnell a strong lead over Democrat Creigh Deeds as polling places closed and the vote-counting began.

A win in Virginia would be a solid opportunity for Republicans a year after Obama became the first Democratic presidential nominee to win the state since 1964.

Democrats were bracing for the unhappy possibility of defeat not just in Virginia but also in New Jersey and in a congressional district in upstate New York where a conservative candidate was leading.

The election outcome could give some clues as to the national mood a year after Obama was elected president and a year before 2010 congressional elections that will represent the first clear referendum on Obama's time in office.

White House spokesman Robert Gibbs dismissed the potential impact of the governors' races on Democrats and the 2010 elections.

"I don't believe that local elections in New Jersey and Virginia portend a lot about legislative success or political success in the future," he said.

While local factors influenced all three races, the weak state of the U.S. economy was an overarching issue that played a role in each state.

Two appearances on Deeds' behalf by Obama appeared to have little impact in Virginia, as Democrats suffered from a lack of enthusiasm without Obama on the ticket. Republicans were energized by the chance to take back the governor's seat, held by Democrats the past eight years.

OBAMA CAMPAIGNS FOR CORZINE

In New Jersey, Republican Chris Christie has been running neck and neck with Democratic Governor Jon Corzine, the former Wall Street executive who has pumped $23 million of his own money into his campaign. A poll released on Monday gave the Republican a slight lead.

Obama campaigned in New Jersey three times for Corzine. His last appearance was on Sunday.

Independent candidate Chris Daggett trailed, and a key question concerned how many of Daggett's supporters would abandon him for Christie or Corzine and sway the race.

New Jersey polls close at 8 p.m. EST (0100 GMT Wednesday) but it could be some hours before the outcome is clear.

While a Virginia loss for the Democrats could be considered fairly predictable in a state long considered a Republican stronghold, a defeat in New Jersey would be seen as a bigger blow to the party because the state leans Democratic. Obama won it by 16 points last year.

"If the Democrats win New Jersey and lose Virginia, I would basically say, no harm, no foul," said Democratic strategist Doug Schoen. "The only real adverse impact is if the administration loses two campaigns, especially one they're heavily invested in New Jersey."

Steny Hoyer, the Democratic leader in the U.S. House of Representatives, said Democratic losses in the governors' races would not slow Obama's domestic agenda in Congress, particularly the battle over a healthcare overhaul.

In New York City, Mayor Michael Bloomberg appeared headed to victory over Democrat Bill Thompson after engineering a rules change to allow him to run for a third term and spending millions of his own money. As of last month, the billionaire mayor had spent $85 million to Thompson's $6 million.

WILD RACE IN NEW YORK

A wild race was taking place in New York's 23rd congressional district for a House seat left vacant when Obama picked Republican John McHugh as his Army secretary.

Conservative Party candidate Doug Hoffman was leading Democrat Bill Owens slightly in the traditionally Republican district. The race took a bizarre twist over the weekend when Republican candidate Dede Scozzafava withdrew because of flagging support and endorsed the Democrat.

Democrats charged the race was an example of how divided the Republican Party has become between conservatives and moderates as it tries to rebound from losing control of Congress in 2006 and the White House in 2008.

Hoffman had been endorsed by conservative Republicans such as Sarah Palin, last year's Republican vice presidential nominee.

In Maine, a "citizen's veto" is on the ballot to overturn a May 2009 law allowing same-sex marriage. If the law is upheld,

Maine would become the sixth U.S. state to allow gay marriage, but the first to approve such a law at the ballot box -- a potential turning point for gay rights after a stinging 2008 defeat in California. Polls close at 8 p.m. EST.

(Additional reporting by Ellen Wulfhorst in New York, Donna Smith in Washington, and Ros Krasny in Boston; Editing by Peter Cooney)