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Senate Democrats will try to move a component of President Obama's $447 billion bill  -- $35 billion in aid to state and local governments to rehire or retain teachers and first responders -- as early as this week, disappointing Republicans who say another piece of the apple would've had a better chance for success.

"Our economy cannot afford to lose any more jobs," Senate Majority Leader Harry Reid, D-Nev., said Monday, vowing to hold a vote "as soon as possible," and promising one provision per week when Congress is in session.

"The bill we are introducing today continues that focus by creating or saving approximately 400,000 jobs for teachers, cops and first responders," the Democratic leader promised.

It's a proposal that has enjoyed bipartisan support in the past, but it is not likely to garner Republican support this time around. Democrats have revived a surtax on Americans making more than $1 million to pay for the bill, a proposal that was largely responsible for tanking the broader jobs bill last week with the entire GOP conference, as well as, two Democrats in opposition.

A senior Senate Democratic leadership aide confirmed to Fox News that Democrats intend to scale the millionaire surtax to pay for jobs measures moving forward. This time the surtax will be .5 percent to bring in the required revenue to make the proposal deficit neutral. Recent polling indicates the tax is popular with Americans.

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"It is disappointing that Senate Democrats are still focused on the same temporary stimulus spending that's failed to solve our jobs crisis instead of bipartisan legislation that would lead to private-sector job growth," said Senate Minority Leader Mitch McConnell, R-Ky, touting the recent passage of three free trade pacts as a preferred, bipartisan path forward to create jobs.

"Democrats have a choice: they can try to divide the country along partisan fault lines for the sake of an election that is still 13 months away, or they can work with us on passing bipartisan legislation -- such as tax reform, domestic energy production, regulatory reform -- that gets at the root of the jobs crisis now."

Calling it a "mini-stimulus," one senior Senate GOP leadership aide predicted the measure's demise, and a McConnell spokesman sent around the transcript of a Reid news conference in 2010 in which he touted a bill that he said at the time "keeps hundreds of thousands of teachers, firefighters ... and other civil employees from being fired or laid off."

But in Reid's conference call with reporters, he noted that 200,000 teachers' jobs were lost in 2010.

When asked to rebut criticism from Republicans that these kinds of state aid programs do not work, Reid replied, "They're absolutely wrong."

"These programs have worked in the past," he said, citing hundreds of thousands of dollars that he claimed "save the government" in Nevada. The leader accused Republicans of having "nothing constructive" to say on jobs, with the main GOP goal of defeating the president in the 2012 election taking precedence.

Meanwhile, Obama continued to push hard for his jobs bill in a campaign-style bus tour to the electorally critical North Carolina and Virginia.

In a speech laced with biting criticism, Obama told a crowd, "It turns out the Republican plan boils down to a few basic ideas: They want to gut regulations; they want to let Wall Street do whatever it wants; They want to drill more. And they want to repeal health care reform," a plan which the president then shorthanded as, "Let's have dirtier air, dirtier water, less people with health insurance."

That ignited an incensed Sen. John McCain, R-Ariz., Obama's 2008 presidential campaign opponent, who appeared on the Senate floor to deliver his own response.

"So the president has taken to the road and, I mean, he spent a number of minutes attacking our plan, and I understand that. I think he has the ... right and privilege to do that. I think the question might be, though, is that appropriate on the taxpayers' dime, since it is clearly campaigning?" Obama's one-time rival asked.

McCain then could not resist a dig, adding, "I must say again, I've never seen an uglier bus than the Canadian one. He's traveling around on a Canadian bus touting American jobs."

The Canadian company Prevost was contracted by the U.S. Secret Service to create two $1.1 million black buses, designed to last 10 years. The interior of the bus is outfitted by an American company located in Tennessee. The GOP's eventual presidential nominee is to occupy one of the busses in the general election.