Democrats in the Senate will this week start to advance elements of President Obama’s $447 billion jobs plan piece-by-piece, challenging Republicans who have already nixed the package as a whole to likewise take vote after vote against its various planks.

They’ll start with a proposal to provide $35 billion for state and local governments for teacher and first responder salaries, an element of the plan Democrats wager will be popular with the public but is also likely to draw particular Republican opposition.

The measure would be paid for with a 0.5 percent surtax on millionaires, similar to the 5.6 percent tax on those making more than a million annually that Senate Democrats had proposed using to pay for the president’s whole jobs package.

Republicans have derided the state funding as a repeat of the 2009 stimulus bill, which also included billions in state aid.

Unlike other elements of the president’s plan which could draw some GOP votes, like extending a payroll tax holiday for workers, the aid for states is likely to face a unified front of Republican opposition.

Which could be part of the point, as Democrats work to sharpen the contrast between the parties as the president’s reelection campaign gets underway.

“Maybe they just couldn’t understand the whole thing all at once,” Obama said of Congress Monday in Asheville, as he kicked-off a three- day bus tour through North Carolina and Virginia in support of the plans. “So we’re going to break it up into bite- sized pieces, so they— they can take— take a thoughtful approach to this legislation.”

“We’re going to give members of Congress another chance to step up to the plate and do the right thing,” he said.

The piece under Senate consideration this week, he said, would offer Congress a choice whether to stand with teachers, firefighters and police officers.

“If they vote against taking steps that we know will put Americans back to work right now. . .then they’re not going to have to answer to me. They’re going to have to answer to you,” Obama said.

The White House has said the money—$30 billion for schools and $5 billion for fire and police forces—could keep 400,000 teachers and first responders on the job.

Republicans counter that the dollars will simply let states shift dollars from their education budgets to other priorities and avoid making tough cutting choices forced by the sluggish economy.

They do not believe the funding will help spur a recovery and say states will have to cut even more deeply after the federal funding runs out and their tax revenues are still not rising.

In a Sept. 16 memo designed to outline possible areas of agreement with the president, House GOP leaders rejected the $35 billion for states outright, saying similar 2009 funding was a “band-aid approach [that] masked over the true fiscal problems facing states and local governments.”

Sen. Minority Leader Harry M. Reid (D-Nev.) told reporters on a conference call Monday that the dollars would help schools that have seen class sizes expand, after school programs ended, art and P.E. eliminated and year-round school halted due to budget cuts.

He insisted the 2009 stimulus measure had indeed slowed the loss of jobs from state and local governments. “These programs have worked in the past. The Republicans know that they've worked in the past,” Reid said.

He said he would bring the bill to the floor Monday and would proceed to a vote soon, as the Senate also juggles an appropriations measure sought by both parties.

“We’ll decide in the next day or so when we’re going to vote,” he said, indicating that he plans to hold one vote a week on difference parts of the president’s plan.

Reid suggested he could keep the Senate in session during a scheduled recess next week to ensure a vote on the jobs bill.

“I am happy to keep the Senate in session as long as needed to make sure we get a vote on this jobs bill,” he said.