WASHINGTON (Reuters) - Both Democrats and Republicans found glimmers of hope for November’s midterm elections amid the political rubble on Wednesday, the day after an anti-establishment wave crashed over the two parties.

Representative Joe Sestak (D-PA) waves to supporters as his carries his 9-year-old daughter Alex alongside his wife Susan Clark-Sestak after declaring victory over Senator Arlen Specter in the Senate democratic primary election at the Valley Forge Military Academy in Wayne, Pennsylvania, May 18, 2010. REUTERS/Beverly Schaefer

In Senate primary elections, disgruntled voters dumped one Democratic senator, Arlen Specter in Pennsylvania, and forced another, Blanche Lincoln, to a run-off in Arkansas in races that Republicans said showed broad anger with President Barack Obama and the Democrats’ policies.

But Democrats touted their win in a special U.S. House of Representatives election in Pennsylvania and took solace in the rout of the Republican establishment choice in favor of a conservative “Tea Party” candidate in Kentucky.

“It was a good news-bad news night for both parties,” said Jennifer Duffy, an analyst with the nonpartisan Cook Political Report. “Voters clearly said to both parties they are not happy with the status quo.”

The House race was the only contest that mirrored November’s elections by pitting the two parties head-to-head -- and Democrat Mark Critz beat Republican Tim Burns by 8 percentage points in a blue-collar Democratic district that backed Republican presidential candidate John McCain in 2008.

It was the kind of swing district both parties must win in November, and the Republican loss raised questions about their ability to benefit from a sour voter mood and gain the 41 Democratic seats they need to claim control of the House.

“It demonstrates that Democrats can compete and win in conservative districts,” Democratic Party chief Tim Kaine said at the National Press Club. “It represented exactly the type of seat Republicans must win this fall if they are to be successful.”

But Republicans noted the Democrat won after distancing himself from Obama and House Speaker Nancy Pelosi and opposing parts of Obama’s agenda. They said the entire Democratic Party would be unable to do that in November, when all 435 House seats, 36 Senate seats and 37 governorships are at stake.

‘AN EARLY PREVIEW’

“This hard-fought race gave us an early preview of what Democrats will attempt to do in the fall in order to survive,” said Representative Pete Sessions, chairman of the House Republican campaign committee.

“They will steer clear of publicly campaigning with President Obama and Speaker Pelosi, distance themselves from the Democratic agenda, and attempt to co-opt Republican positions on the issues,” he said.

The loss by the six-term veteran Specter was a setback for Obama, who visited Pennsylvania on his behalf last September. A Specter television ad used his quote from that visit: “I love Arlen Specter.”

Republicans said they could take advantage in November of Obama’s unpopularity in conservative areas. Rand Paul, the conservative “Tea Party” favorite who beat a handpicked Republican establishment candidate in a Kentucky Senate primary, practically taunted Obama after his win.

“Please bring President Obama to Kentucky, bring him to campaign as much and as often as they can because he’s incredibly unpopular here,” Paul told Fox News Channel. “Bring it on.”

Paul rode to victory on the anger of grass-roots Tea Party activists who oppose runaway government spending and favor more limited government. Democrats hoped his win could open the door for their more moderate candidate, state Attorney General Jack Conway.

Kaine said the win by Paul -- and the recent defeat of Utah Republican Senator Bob Bennett by Tea Party activists -- was a sign of a Republican civil war that could have long-term benefits for Democrats.

“In order to satisfy Tea Party activists, Republicans are running to the right. As moderates are eliminated, the Republican Party will become less and less appealing to independents and other swing voters,” he said.

Slideshow ( 18 images )

Wall Street analysts expressed concern the anti-Washington mood would lead both parties to pick more extreme candidates, raising the risk of gridlock on Capitol Hill when policymakers say unified action is needed to tackle the budget deficit.

“It seems to be the more extreme wings of either party who are winning and are not necessarily going to be fiscally responsible,” said John Canally, an investment strategist and economist for LPL Financial in Boston.

While the primaries are about appealing to the extremes, the November election would focus on winning the broad middle, said Stephen Wayne, a political analyst at Georgetown University.

“Voters who turn out in general elections are less ideological as a whole than in the primaries,” he said. “You see polarization in primaries -- you won’t see it as much in the general election.”

The next political showdown comes on Saturday in another special House election in a Democratic district in Hawaii.