Senate Majority Leader Harry Reid moved quickly to shore up support in his Democratic caucus for President Barack Obama’s jobs bill Wednesday, announcing it would come to the Senate floor shortly and be paid for by a surtax on millionaires.

Reid’s decision to pay for the $447 billion package with a 5.6 percent surtax on income of more than $1 million starting in 2013 gives Democrats a poll-tested package that most can run on for the next year — even though the surtax itself is dead on arrival with Republicans.

Indeed, Reid appears to be setting the stage for a major floor battle that will raise the specter of “class warfare” and Obama recently called himself a “warrior for the middle class.” Democrats have been feeling less vulnerable on the issue of raising taxes on the rich because recent polls, such as an Oct. 3 CBS News poll, have shown that two-thirds or more of Americans believe millionaires should pay more into federal coffers.

Still, Reid predicted “most all” — though not all — Democrats would support it.

For example, Sen. Ben Nelson (D-Neb.) has said he would vote to block any bill containing a tax increase — and others have also been skittish about tax hikes.

The announcement came less than a day after Senate Minority Leader Mitch McConnell (R-Ky.) sought a vote on Obama’s original package, with the intended purpose of killing it quickly and exploiting divisions among Democrats over how to pay for the plan.

McConnell’s maneuver forced Democrats to accelerate their timetable for crafting a specific package, lest they get blamed for blocking a vote and mess up their general attack line that “do-nothing” Republicans are thwarting the president.

Reid said at a press conference that the millionaire tax has broad, bipartisan support across the country. “Seventy-five percent of Republicans support this tax,” Reid said. “The problem is none of them are in the Senate.”

Reid said that if Republicans cling to their no-new-taxes mantra, “they are not keeping in touch with their constituents.”

If Republicans block the bill, they will be putting “tax breaks for millionaires and billionaires ahead of our economic recovery,” said Sen. Charles Schumer (D-N.Y.), the party’s messaging chief. Schumer said the White House was “fine” with the millionaire tax instead of the assortment of tax increases that it originally proposed.

Schumer said drawing the line at $1 million “is the right thing to do,” instead of Obama’s original proposal to tax couples making more than $250,000 a year. Citing a rationale Republicans have used in the past, Schumer said there are too many struggling small-business owners with incomes of less than $1 million and many people making $250,000 a year who “are not rich” in many parts of the country.

Republicans, meanwhile, blasted the proposal as another tax increase that would hurt the economy, particularly because it was originally slated to take effect in 2012. However, the bill that Reid introduced late Wednesday was revised to change the effective date to 2013.

“There they go again: Washington Democrats insisting on raising taxes on job creators right now,” House Majority Leader Eric Cantor (R-Va.) told Bloomberg TV earlier in the day. “That is not what we need. I think most people think it is counterintuitive to raise taxes if you want economic growth.”

Republican aides sent around various statements from Democrats who have opposed tax increases over the past few years.

A senior Democratic aide said Wednesday that Democrats would like to work with Republicans on a way to pass the jobs bill but that the GOP has shown no interest in doing so. In the meantime, Democrats are going to try to make the GOP pay a political price.

A vote is likely early next week on the jobs bill, which is expected to fail. Democrats then likely will take up three free-trade agreements and appropriations bills before forcing another vote on the jobs package.

The idea is to make the GOP vote again and again to thwart the plan in hopes that it will budge — or pay a political price.

If Democrats can’t break the GOP with multiple votes — a scenario that is unlikely — they might eventually move toward breaking the bill into chunks and voting on pieces such as the payroll tax cut extension that some Republicans have backed.

Democrats can then attack the GOP if it stands firm and allows a tax hike to hit the middle class in January when the existing 2 percentage point payroll tax cut expires.

Sen. Jim DeMint (R-S.C.) said Democrats don’t want to work with Republicans on a jobs package. “I don’t think they want to pass anything because then they are going to accuse Republicans of obstructing a jobs plan, and they are going to try to say the economy is Republicans’ fault.”

DeMint predicted many Republicans would oppose a payroll tax cut even if it is not offset with spending cuts elsewhere.

“It would be hard for us … but I think a lot would vote against it if it were not offset. It’s making our problem worse, our debt hole deeper.”

DeMint acknowledged that’s a shift from the past, when the GOP has supported tax cuts that increased the deficit.

“The problem is so much worse, we’re having to borrow so much money every month … so offsetting is pretty critical,” he said.

Editor’s Note

The online version of this story was updated to reflect the revised version of President Barack Obama’s jobs bill that Senate Majority Leader Harry Reid (D-Nev.) introduced after Roll Call’s deadline Wednesday. The introduced bill includes a higher surtax on income of more than $1 million than Obama had proposed, 5.6 percent versus 5 percent, and it would go into effect a year later, in 2013.