President Barack Obama has a Virginia problem.</p><p>And a New Jersey conundrum.</p><p>Voters in those states head to the polls Tuesday in off-year elections to choose governors in what amounts to the Democrats&rsquo; first big electoral test since Obama swept to power a year ago.</p><p> If Republicans win both races, Obama will take a huge political hit &mdash; whether it&rsquo;s deserved or not.</p><p> &ldquo;The perception is that it&rsquo;s a very big deal,&rdquo; said Joe Aistrup, a political science professor at Kansas State University. &ldquo;The perception is if the Democrats get swept by the Republicans, that will be a harbinger for 2010.&rdquo;</p><p> Even though the focus in both races is largely on local issues, their results could provide Republicans with a rallying cry that better days are ahead for a party that has been in disarray.</p><p> Also on the ballot Tuesday is a special congressional election in upstate New York that offers Obama a possible lifeline. The contest pits a Democrat against a Conservative Party contender. Republican candidate Dede Scozzafava withdrew from the race Saturday after trailing in polls behind Democrat Bill Owens and Conservative Party candidate Doug Hoffman. A victory by Owens would give Democrats a rare win in outstate New York.</p><p> But the marquee races are in Virginia and New Jersey, where Obama made campaign stops in recent days.</p><p> Obama carried Virginia in 2008, the first time in 45 years that a Democrat had won the state. </p><p>In the race for governor, Republican Robert McDonnell faces Democrat Creigh Deeds. It is a rematch of their 2005 squeaker of an attorney general race, which McDonnell won by 360 votes out of almost 2 million cast.</p><p> The latest polls show McDonnell leading by 13 to 18 percentage points. Obama tried to turn the tide Tuesday at a rally in Norfolk, where he sought to stamp out Democratic complacency after last year&rsquo;s highly emotional election.</p><p>&ldquo;I don&rsquo;t believe in &lsquo;can&rsquo;t,&rsquo;&ensp;&rdquo; Obama said. &ldquo;I don&rsquo;t believe in giving up. &hellip; I know there are a lot of folks out here. They came out in November for my campaign &hellip; but these sort of off-year elections, you know, sometimes people say, &lsquo;Well, you know, I just went last year. I was volunteering. I already did that knocking on doors.&rsquo;</p><p> &ldquo;So maybe people feel a little bit complacent, maybe feel a little cynical because they&rsquo;re thinking, &lsquo;Well, we haven&rsquo;t changed things overnight.&rsquo;&ensp;&rdquo;</p><p>Last month, Deeds was asked in a debate whether he was a &ldquo;Barack Obama Democrat.&rdquo;</p><p>He responded, &ldquo;I would try to escape that by saying I&rsquo;m a Creigh Deeds Democrat.&rdquo; Deeds conceded that &ldquo;a lot of what&rsquo;s going on in Washington has made it very tough.&rdquo;</p><p> History is running solidly against the Democrats. Since 1977, Virginians have elected only governors from the party that <em>wasn&rsquo;t </em>occupying the White House. That is one reason some analysts downplay the significance of this election.</p><p> Another reason: While Obama clearly has injected himself into the races, most of the campaign talk in both states has been local issues &mdash; property taxes, public corruption and failing schools in New Jersey, transportation and crime in Virginia.</p><p> &ldquo;Neither of these races has really focused on either Obama or federal issues,&rdquo; said Jennifer Duffy, an analyst for the nonpartisan Cook Political Report.</p><p> In New Jersey, Christopher Christie, a former U.S. attorney, is challenging the incumbent, Democratic Gov. Jon Corzine. Christie blames Corzine for many of the state&rsquo;s fiscal problems. Corzine counters that they were part of the national economic downturn.