Senate Majority Leader Harry ReidHarry Mason ReidHarry Reid calls on Democrats to plow forward on immigration Democrats brace for tough election year in Nevada The Memo: Biden's horizon is clouded by doubt MORE (D-Nev.) signaled on Tuesday that he and other Senate Democrats are looking to advance President Obama's proposal to spend $35 billion to shore up jobs for teachers, police and firefighters in the coming weeks.

Reid, Sen. Robert MenendezRobert (Bob) MenendezWhy is Trump undermining his administration's historic China policies? Senate GOP signals they'll help bail out Biden's Fed chair Democrats weigh changes to drug pricing measure to win over moderates MORE (D-N.J.) and other Senate Democrats on Monday introduced the Teachers and First Responders Act, which mirrors the plan Obama has been touting in a bid to get Congress to pass pieces of his American Jobs Act. Under the proposal, $30 billion would be used to shore up 400,000 teacher jobs, and another $5 billion would go for thousands of police and firefighter jobs.

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Reid said Tuesday that the bill, S. 1723, is "fully paid for," but said rather than cuts to other federal programs, it would raise taxes on the wealthy.

"It asks millionaires and billionaires to contribute a tiny fraction more to help turn our economy around," he said. On Monday, Reid stressed that this is "not deficit spending. This is money that will be paid for."

Specifically, Sen. Dick DurbinDick DurbinPatience wears thin as Democrats miss deadlines 535 'presidents' with veto power: Why budget deal remains elusive After 35 years, Congress should finally end the sentencing disparity between crack and powder cocaine MORE (D-Ill.) said Tuesday morning that the bill would be paid for by requiring people earning more than $1 million per year to pay about one half of one percent more in taxes.

Democratic supporters say the bill is needed because about 300,000 teacher jobs have been lost since 2008. Menendez said in introducing the measure that failing to pass it puts at risk "the future of our children and the safety of our communities."

But these claims prompted Senate Republicans to point out that Obama and other Democrats promised over the last two years that they would save teacher and first-responder jobs by approving the $787 billion stimulus bill in 2009, and a 2010 bill giving states additional aid.

Senate Republicans argued that this shows federal stimulus programs are not working at all, and put out a release titled "So the last two didn't work?"

Reid said on Monday that he would try to approve the bill this week, but acknowledged that this could be difficult, and said he could decide to cut short the Senate's planned recess next week to get the work done. Otherwise, work on the bill would be delayed until the Senate returns in early November.

-- This story was updated at 12:11 p.m. to clarify the timing of the bill.