Republican Bob Turner, who won Tuesday’s special election in New York's heavily Democratic 9th District, speaks with the media at a polling station on Sept. 13, 2011 in New York City. (Photo by Spencer Platt/Getty Images)

At a closed-door meeting with House Democrats Wednesday afternoon, House Minority Leader Nancy Pelosi (D-Calif.) and Democratic Congressional Campaign Chairman Chairman Steve Israel (N.Y.) told members to keep their eyes on races beyond Tuesday’s special elections.

“The message was, ‘Look beyond this election,’” said Rep. Jan Schakowsky (D-Ill.), a member of the Congressional Progressive Caucus. “It’s not going to affect our taking back the House.”

“This district was never calculated in that math of our effort forward, and we need to just take the cautionary lessons from that to be ready for competitive races.”

Schakowsky also made clear that House Democrats would be stumping on the Medicare mantra going forward, referring to Rep. Paul Ryan’s (R-Wis.) plan to convert Medicare to a voucher system by 2012.

“They can call it whatever they want -- ‘Sortacare,’ ‘Maybecare,’ ‘Idontcare,’” Schakowsky said. “But their proposal was not Medicare. It was not a program with guaranteed benefits. And so, I think this continues to be a very powerful issue.”

As for Republicans, they crowed about the win in a solidly Democratic New York seat that hasn’t gone GOP in a century.

“How do you print a smile?” responded Rep. Dave Camp (R-Mich.) about the GOP’s double victories. “I look at it as a referendum on the administration’s policies, frankly.”

But the White House denied fears that the claiming of New York’s 9th district, which belonged to retired Rep. Anthony Weiner (D-N.Y.), was a referendum on Obama’s presidency.

“Special elections are often unique and their outcomes do not tell you very much about future regularly scheduled elections,” Jay Carney, the White House press secretary, told reporters Wednesday aboard Air Force One.

“And I’m sure that you and everyone else here did not write, after Democrats won all, I believe, the special elections in 2009 and 2010, that that foretold a certain outcome in the 2010 midterms. Certainly, this election has no other bearing.”

Rep. James Clyburn (S.C.), the No. 3 Democrat in the House, said that the message he gleaned from Tuesday’s New York loss was that “we’ve got a lot of work to do before the next national elections; there’s no question about that.”

Clyburn pointed in particular to the district’s large Orthodox Jewish population, which largely opposes Obama’s position on Palestinian statehood.

“People are frustrated,” he said. “There are a lot of Orthodox Jews who make no secret of the fact that they don’t like President Obama’s position on being for a two-state resolution there. That’s a fact. A lot of them don’t like the fact that he supported the building of the mosque there. They don’t like the fact that there are jobs to be created there. So the confluence of all of that provided a perfect storm for these results.”

“But remember,” Clyburn added, “the district goes away in about 14 months.”

Clyburn is referring to the fact that the largely Democratic 9th district, based in Queens, is on the chopping block in 2012 because the Empire State is slated to lose two seats in redistricting.

“It’s very easy to over-read the results of these elections as a catastrophic event,” said Bill Burton, Obama’s former deputy press secretary who has since co-founded Priorities USA Action, a political action committee. “That said, there is no part of me that does not think the fall elections will not be very difficult for the president. But we didn’t need a special election to tell us that. We have the economy.”

Asked how nervous Democrats are following the special election defeats and recent polls showing Obama’s approval rating at new lows, Burton said, “Probably not nervous enough.”

“Democrats need to know that this is going to be a very tough election for President Obama, and unless people get engaged, it could be catastrophic,” he said.

The main problem, Burton said, is that too many Democrats are not taking the Republican field seriously given some of the positions candidates have staked out - on Social Security and Medicare, for example - that could turn off crucial independent voters.

“They think, ‘These guys can’t beat President Obama,’’ Burton said. “But let me tell you - in a close election, any Republican can.”

Making Medicare a centerpiece of the 2012 campaign could also be dangerous for Democrats should the 12-member debt supercommittee, which includes Democrats and Republicans, craft a plan that includes reforms of entitlement programs such as Medicare, Medicaid and Social Security.

Schakowsky said Wednesday that she believed her party would be able to effectively highlight the differences between Democrats and Republicans regardless.

“I’d be all for it if the supercommittee were to say Medicare needs to negotiate with the pharmaceutical companies for lower drug prices, and we could save over ten years over $200 billion by doing that kind of thing,” she said. “But taking Medicare and its guaranteed benefits away from seniors... that’s not on the table.”

In Tuesday’s elections, Republicans held the seat of former Rep. Dean Heller (R) in Nevada and capture former Rep. Anthony Weiner’s (D) Queens-and-Brooklyn-based district — which has voted Democratic for nearly a century.

Businessman Bob Turner (R) defeated Assemblyman David Weprin (D), 53 percent to 47 percent in New York, while former state Sen. Mark Amodei (R) bested state Treasurer Kate Marshall (D), 58 percent to 36 percent, in Nevada.

House Republican leaders claimed that the dual victories were a referendum on national Democrats and President Obama’s stewardship on the economy as the country’s unemployment rate hovers above 9 percent.

“Tonight New Yorkers have delivered a strong warning to the Democrats who control the levers of power in our federal government,” House Speaker John Boehner (R-Ohio) said. “It’s time to scrap the failed ‘stimulus’ agenda and the misguided policies on Israel and focus on getting America back to creating jobs again.”

Boehner said that with Amodei’s victory in Nevada, voters “sent a strong message that they want to stop runaway Washington spending and get America back to creating jobs again.”

“This special election couldn’t come at a more important time as Congress begins to consider the President’s economic plan,” he added.

And just as they did during the 2010 cycle, national Republicans in the wake of the New York and Nevada wins Tuesday kept their message focused on both Obama and Pelosi, who was ousted from the speakership when Republicans recaptured the House in November after an election that saw Republicans’ campaign arms run scores of TV ads tying local candidates to the House’s top Democrat.

“This clear rebuke of President Obama’s policies delivers a blow to Democrats’ goal of making Nancy Pelosi the speaker again,” National Republican Congressional Committee Chairman Pete Sessions (Texas) said in a statement on the New York race. “New Yorkers put Washington Democrats on notice that voters are losing confidence in a President whose policies assault job-creators and affront Israel. An unpopular President Obama is now a liability for Democrats nationwide in a 2012 election that is a referendum on his economic policies.”

Amodei’s victory in Nevada, Sessions said, hinged on “his commitment to cut deficit spending, taxes and regulations to free Nevada small businesses to grow and hire more workers” — all themes that congressional Republicans have made a central part of their agenda on Capitol Hill this fall.

“Special Elections are always difficult — they are low turnout, high intensity races,” DCCC Chairman Israel said in a statement early Wednesday.

Israel added that the results of the race between two non-incumbents in New York “are not reflective of what will happen in November 2012 when Democratic challengers run against Republican incumbents who voted to end Medicare and cut Social Security while protecting tax loopholes for big corporations and the ultra wealthy.”

“When Republican incumbents’ records are tested, the American people will vote for a Democratic candidate committed to creating jobs and protecting Medicare and Social Security,” he said.

White House press secretary Jay Carney echoed the House Democratic line Wednesday, saying that special contests are unique and don’t say much about future elections. He added that the White House doesn’t view the race as a referendum on Obama’s presidency.

Some Democrats on Capitol Hill Wednesday argued that the New York race was about voters’ dissatisfaction with both parties when it comes to working together to resolve the country’s economic woes.

“Of course, there’s lots of messages being sent,” Sen. Barbara Boxer (D-Calif.) said. “There was a message sent from upstate New York [in May]; there’s a message sent now -- we have to get together and work together. And what the president did is, yes, he put together a bill. Each of us could put together a different bill. But he has an eye on getting this done. ... There is no time to wait.”

Other Democrats downplayed their party’s losses by contending that national issues were not at play in either race.

“I’m sure the Republicans are going to want to spin it as another example of, ‘It’s going to be a bad year for the president, a bad year for the Democrats,’” said Rep. Heath Shuler (D-N.C.), co-chairman of the conservative Blue Dog Coalition. “I would disagree. If you look at Nevada, I think most people would tell you it was going to go Republican.... New York, there were a lot of local issues involved.”

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Scott Wilson contributed to this report