WASHINGTON (AP) — In a very early test of President Barack Obama's political influence, two states are choosing whether to continue Democratic rule while voters elsewhere elect a handful of congressmen and big-city mayors.



Elected just a year ago, the president has spent a considerable amount of time and energy trying to ensure that Democrats win governor's races in Virginia and New Jersey and pick up a GOP-held congressional seat in upstate New York.



In doing so, Obama raised the stakes of a low-enthusiasm off-year election season — and risked political embarrassment if any lost.



All three could.



Heading into Tuesday's elections, Democrat gubernatorial candidate R. Creigh Deeds was trailing Republican Bob McDonnell in polls by double digits in Virginia. In a three-way race in New Jersey, Democratic Gov. Jon Corzine was in a close race with Republican Chris Christie and independent Chris Daggett. And in the race to fill the vacant 23rd Congressional District seat in New York, Democrat Bill Owens was in a tight fight with conservative Doug Hoffman after the GOP's hand-picked candidate bowed out over the weekend.



Elsewhere, California Lt. Gov. John Garamendi is expected to maintain the Democratic Party's hold on the open 10th Congressional District seat near San Francisco, while New York Mayor Michael Bloomberg is expected to cruise to a third term. Atlanta, Houston, Boston, Detroit and Pittsburgh also will elect mayors, while voters in Maine and Washington weigh in on same-sex unions and voters in Ohio decide whether to allow casinos.



To be sure, it's easy to overanalyze the results of such a small number of elections in a few places. The results will only offer hints about the national political landscape and clues to the public's attitudes. And the races certainly won't predict what will happen in the 2010 midterm elections.



"The results of these elections tend to be overread," former Obama campaign manager David Plouffe said Tuesday on NBC's "Today." ''These are local races. There's 18,000 lifetimes between now and next November."



But, given that Democrats control the White House and Congress, defeats in Virginia — a new swing state in national elections — or New Jersey — a Democratic stronghold — would be setbacks for the White House, even though both states having long histories of electing governors from a political party opposite that of the president.



After all, this is a president who won a year ago in an electoral landslide after building a fundraising and organizational juggernaut that attracted scores of new voters into what Obama loyalists have called a movement. And this is a party that has comfortable majorities in the House and Senate — and that controls governor's mansions in Virginia and New Jersey.



As the Democratic Party chief, Obama had little choice but to work hard to elect Corzine and Deeds; doing otherwise would have been seen by the base as a breach of duty.



So, he campaigned several times for Corzine and raised money for Deeds. Obama also was featured in campaign advertisements for both. He characterized the success of their candidacies as key components for the White House to make good on its political promises and advance its agenda. And he deployed the Democratic National Committee and his own political campaign arm, Organizing for America, to ensure the swarms of new voters he attracted in 2008 turn out even if he's not on the ballot.



Of the two races, a Republican victory in Virginia would be the most telling about potential trouble ahead for Democrats as they compete in swing states next fall.



Long reliably Republican in national races, Virginia is a new swing state. It's home to a slew of northern bellwether counties filled with swing-voting independents who carried Obama to victory last fall, the first Democrat to win the state in a White House race since 1964. Rapidly growing counties like Loudoun and Prince William swung toward Democrats in the 2005 governor's race, previewing an Obama win three years later.



Conversely, New Jersey is a traditional Democratic-leaning state with an incumbent Democratic governor. As such, it's the trickier of the two for Republicans to win — and yet the GOP just might.