President Barack Obama's Democrats and his Republican opponents enter the 2010 election season facing voters in an anti-incumbent mood over the sour U.S. economy, increasing the political pressure on both sides.

A 10.2 percent jobless rate for October that is still rising despite expensive government programs hurled at it, is dominating the political debate outside Washington and poses challenges for legislators who face re-election next November.

The mood of America is glum, the Pew Research Center said this week in a poll that found two-thirds of Americans are dissatisfied with the way things are going in the country.

Republicans believe conditions are ripe for making deep inroads into strong Democratic majorities in the House of Representatives and the Senate in elections, when all 435 House seats and one third of the 100-member Senate are up for grabs.

After all, under this reasoning, the party in power usually loses seats in the first congressional elections after a new president takes office.

The Pew poll found that 52 percent of registered voters would like to see their own representative re-elected next year, a measure that is among the most negative in two decades of Pew Research surveys.

But Republicans face their own obstacles, including a deep divide between conservatives who are the base of the party and moderates, Democratic criticism that by rejecting Obama's policies they have not joined in the search for solutions to big problems after being bested in elections in 2006 and 2008.

To be sure, any time the economy is hurting, the climate for incumbents of any party is always going to be difficult, said Phil Singer, a Democratic strategist who advised Hillary Clinton's presidential campaign last year.

They reason why I'm not too worried about our electoral prospects is that the Republicans have a flawed strategy. They're taking a 'throw the bums' out approach that doesn't work when the people making the argument are the bums that got thrown out a year earlier, he said.

TARGETING OLD DISTRICTS

Republicans believe they will do well regardless and have targeted those congressional districts where Democrats were elected in recent years but have traditionally been held by Republicans.

They point to Republican victories earlier this month in governor's races in Virginia and New Jersey as indicative of a resurgence, and dismiss fissures in the party manifested by a New York congressional race in which a conservative lost to the Democrat after the Republican candidate withdrew.

I come from the school that the intraparty split is fine because the strongest ideas will win at the end of the day, said Republican strategist Scott Reed.

As long as these are debates about ideas, and not personalities, that is to the benefit of the party, and if you're the out party it's a good time to have a robust debate about ideas and a forward-looking agenda and usually the strongest survive, he said.

Democrats have their own concerns to worry about.

Obama, under pressure to create jobs, announced as he left on a week-long Asia tour that he will host a White House jobs conference in December that brings together corporate chiefs and small business owners.

He said that despite a rise in the stock market and other indications of a healing economy, millions of Americans -- our friends, our neighbors, our family members -- are desperately searching for jobs.

While voters are expressing an anti-incumbent mood now, political analysts say it is far too soon to write off Democrats in 2010.

The point is the public isn't mad at Democrats in Congress, the public is mad at Congress, said Linda Fowler, a professor of government at Dartmouth College in New Hampshire. I'm a skeptic about whether any of this means anything right now.

(Editing by Arshad Mohammed and Philip Barbara)