Opposition Democrats are claiming newfound political momentum in the wake of victories in governor's races Tuesday in Virginia and New Jersey. Republicans, meanwhile, are taking issue with the notion that the election results are a rebuke to President Bush.

In Virginia, Democrat Tim Kaine defeated Republican Jerry Kilgore in a race that could have national implications.

"We did it. We did come together, Democrats and Republicans," said Mr. Kaine.

Mr. Kaine, the current lieutenant-governor, won despite a last-minute campaign appearance by President Bush on behalf of Republican Jerry Kilgore.

"Turn out that vote and you will be proud of the next governor of Virginia, Jerry Kilgore," Mr. Bush said.

Democrats argue that the president's low approval ratings may have hurt the Republican candidate in Virginia. They also say the Kaine victory is a boost for Virginia's outgoing Democratic governor, Mark Warner, who is considering a run for president in 2008.

Democrats got more good news in the northeastern state of New Jersey where Senator John Corzine easily won the governor's race over Republican Doug Forrester.

"I want to thank the people of New Jersey for rejecting the Bush- [Karl] Rove tactics that we see in politics," said Mr. Corzine.

But in fact, New Jersey voters complained that both candidates conducted negative campaigns and spent millions of dollars of their own money in the governor's race. Republicans cautioned not to read too much in the way of national implications in the Virginia and New Jersey defeats.

White House spokesman Scott McClellan said the races were decided on local issues and candidates. He also said the Virginia winner, Tim Kaine, ran as a conservative and that the national Democratic Party is out of touch with voters.

"In these two specific races, you have very personality-based races and that sort of precluded [prevented] the situation of the country or the image of the president from being a key role in this," said David Winston, a Republican pollster based in Washington.

But, Democrats say they hope to build on the 2005 results to make gains in next year's congressional elections in which the entire House of Representatives, one-third of the Senate, and 36 governorships will be at stake.

"It is because we had great candidates," said Howard Dean, the Democratic Party's national chairman. "They took nothing for granted, they asked everybody for their vote and they had more to say about the new direction for the country than the Republicans did and that is exactly the blueprint for Democrats winning elections and it is great to start winning them again."

Some political analysts say that Republicans should be concerned about President Bush's low public approval ratings as they look ahead to the 2006 mid-term elections.

Larry Sabato heads the Center for Politics at the University of Virginia. He spoke on CBS television.

"We do not know what the conditions will be in 12 months," he said. "But I will tell you this, either President Bush improves his approval rating and everything that comes with that substantially and gets to at least 50 percent or so in the polls, or the Republicans will have a hard time holding what they have got, much less making gains [in the 2006 congressional elections]."

In other races, New York City Mayor Michael Bloomberg, a Republican, easily won a second term in that heavily Democratic city. Out west, California Governor Arnold Schwarzenegger suffered a political setback when voters rejected four ballot measures he was backing in a bid to control state spending.

Governor Schwarzenegger is also hampered by low public approval ratings as he prepares to seek re-election next year. Voters in Texas overwhelmingly approved a constitutional ban on homosexual marriage. But in the northeastern state of Maine, voters rejected an attempt to strike down a new law making it illegal to discriminate on the basis of someone's sexual orientation.