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By returning to Washington to give the green light to another round of taxpayer-funded state aid, congressional Democrats are betting voters will reward, rather than punish, them for helping their cash-strapped states cover the costs of health care programs and teachers’ salaries.

With the House abruptly interrupting its month long recess for Tuesday’s debate and vote, Democrats are casting the $26.1 billion plan as a win-win proposition.

They say the bill does not add to the national debt and - in overcoming Republican opposition - they have saved the jobs of tens of thousands of teachers, firemen and police nationwide.

“Why wouldn’t House Republicans want to keep 310,000 teachers, first-responders and private-sector workers on the job instead of on the unemployment lines?” House Speaker Nancy Pelosi, California Democrat, said Monday.

Mrs. Pelosi made her comment a few days after the Department of Labor released a report showing that the country had shed 131,000 jobs last month.

But GOP leaders have been quick to point up the political risks of the special vote to approve more government spending, in the face of voter sentiment for the government to tighten its belt.

“The American people are screaming at the top of their lungs to Washington, ‘Stop, stop the spending, stop the job-killing policies,’ and yet Democrats in Washington refuse to listen to the American people,” House Minority Leader John A. Boehner, Ohio Republican, said Sunday on NBC’s “Meet the Press.”

On Tuesday, the Democrat-controlled House is expected to pass the measure, which in part relies on ending foreign tax credits for multinational companies and money from last year’s stimulus bill to pay for $10 billion in teachers’ salaries and $16.1 billion for the extension of the Federal Medicaid Assistance Program (FMAP). More than a dozen states are counting on the money to balance their budgets and to keep about 140,000 teachers nationwide on the payroll.

Rep. Chris Van Hollen last week shrugged off the suggestion that approving the measure might come back to haunt the party in the midterm elections this fall.

“It is not a gamble,” the Maryland Democrat told The Washington Times. “It would be gambling our children’s education to have them go back to school and find no teacher in the classroom and with larger class sizes.”

Senate Democrats approved the plan last week on a 61-39 vote after Sens. Olympia J. Snowe and Susan Collins, Maine Republicans, helped to break a GOP-led filibuster and advance the bill to the Senate floor for a vote.

Faced with an unemployment rate hovering at 9.5 percent and the bad news from the Department of Labor, political observers say, Democrats are aiming to reframe the political debate and to put Republicans on the defensive.

Isaac Wood of the Center for Politics at the University of Virginia pointed to a recent Pew Poll that, in his words, found “despite some of the idealistic rhetoric, voters overwhelmingly prefer congressmen and senators who bring home the bacon.”

“This bill is yet another way for incumbents to show how they’ve delivered for their districts and their states,” Mr. Woods said. “Democrats desperately need concrete legislative accomplishments on economic issues and this would serve as a notch in that belt. It would also help mute some of the criticism about only big corporations getting government bailouts.

“On the other side of the coin, if the economy remains dour, Republicans can point to this as even more billions of dollars down the drain with no positive impact felt by average Americans,” he said.

The dueling messages have been on display in recent days - perhaps providing a sneak preview into the campaign messages the parties will employ this fall in an election that will decide whether Democrats retain control of both chambers of Congress.

Rep. Joe Sestak, Pennsylvania Democrat, has hammered his opponent in the coming U.S. Senate race, Republican Pat Toomey, a former three-term congressman, because he voiced opposition to the FMAP and teacher funding package.

“Congressman Toomey’s out-of-touch philosophy was on display again yesterday when he publicly opposed deficit-neutral aid to states that would prevent massive layoffs and cuts to essential service,” Mr. Sestak’s campaign said in a statement.

Asked whether this line of attack would continue as the campaign season heats up, Sestak spokesman Jonathon Dworkin told The Times, “We will certainly point out that this issue is another example of Congressman Toomey’s rigid mindset that favors benefits for the wealthiest, but opposes creating opportunities for the middle class.”

Toomey spokeswoman Nachama Soloveichik fired back by calling the bill a “bailout for irresponsible states” that spent recklessly when times were good and “now that they’ve run out of money, they’re running to the federal government to force taxpayers to bail them out.”

Mr. Sestak “voted for the Wall Street bailout, the auto bailout, the bailout of Fannie Mae and Freddie Mac, so it is not surprising that he has another opportunity to vote for a bailout and he says, ‘Sign me up,’ ” she said.

Party leaders continued to trade political barbs Monday.

Mrs. Pelosi criticized Republicans who had opposed the state aid while pushing to preserve expiring tax cuts for Americans in the top income brackets. The cuts were approved under President George W. Bush.

“With jaw-dropping indifference to America’s teachers and police officers, the GOP is calling for an extension of the deficit-busting Bush tax cuts for the wealthiest few and saddling Americans with nearly $700 billion in debt over a paid-for bill that creates 310,000 jobs for hard-working Americans,” the California Democrat said in a press release.

Mr. Boehner’s office characterized the bill as a payoff to union bosses and liberal special interests.

“This spending was a direct order from Washington unions to Democratic leaders, and people will remember that Democratic members listened to union bosses and their liberal leadership rather than their constituents, who want to stop the spending and end the bailouts,” said Michael Steel, Mr. Boehner’s spokesman.