* Democrats say the politics are on their side
* Will advance Obama's jobs bill in pieces
By Andy Sullivan and Alister Bull
WASHINGTON, Oct 12 (Reuters) - Fresh from a defeat at the hands of Republicans, President Barack Obama and his fellow Democrats said on Wednesday they will move their jobs bill in pieces to convince voters that they are a better choice to spur the sluggish economy.
One day after Republicans blocked the $447 billion job-creation package in the Senate, Obama said he was not giving up.
"We will keep organizing and we will keep voting until this Congress finally meets its responsibilities," Obama told a Hispanic forum in Washington.
Senate Democratic leaders said they will hold votes on individual components of the package over the coming months, to convince voters that Republicans are preventing the government from taking action to lower the 9.1 percent unemployment rate.
"It's a win-win for us. If they support us, we get something done for the economy," Democratic Senator Charles Schumer said at a breakfast roundtable. "The idea that Republicans seem to want to block everything and have no ideas, that Tea Party economics is dominating what they do, I think will bode very well for us in 2012."
Obama's re-election chances next year may hinge on whether he can convince voters he is helping the U.S. economy dig out from the worst recession since the 1930s. Democrats also face tough odds as they try to hold on to their Senate majority and win back the House of Representatives from Republicans.
Democrats have spent much of the year playing defense as Republicans aligned with the conservative Tea Party movement have won record spending cuts in a series of high-stakes budget battles.
With the economic recovery stalling out, Democrats have sought to shift the focus from austerity back to stimulus. Obama has spent the past month barnstorming around the country, pressuring Republicans to back his package of tax cuts and new spending in order to bring down the jobless rate.
Its defeat on Tuesday has given Democrats new ammunition.
"Republican obstructionism has once again cost this nation millions of jobs," Senate Democratic Leader Harry Reid said on the Senate floor. "It seems as if Republicans don't really want to put Americans back to work.
Republicans say Obama is more interested in demonizing them than working together on free-trade agreements and other economic measures that can actually pass Congress.
"If President Obama were willing to work with us on more bipartisan legislation like this, nobody would even be talking about a dysfunctional Congress. There wouldn't be any reason to," Senate Republican Leader Mitch McConnell said.
"But, as we all know, that doesn't fit in with the President's reelection strategy. The White House has made it clear that the President is praying for gridlock," he said.
Republicans have coalesced around a job-creation agenda of their own centered on rolling back pollution rules and other regulations on business.
Senate Democrats said they have not determined yet which pieces of Obama's defeated bill they will bring up for a vote starting next month, or whether the pieces will be paired with tax increases on the wealthy or other tax hikes to offset the cost. They may offer ideas of their own as well.
Republicans have backed some components of the package, such as a payroll tax cut, in the past, but have not said whether they will do so again. Payroll taxes, paid by every U.S. worker, are set to rise at the end of this year if Congress does not act, which could create additional headwinds for the struggling economy.
Republicans are certain to reject other components, such as $120 billion in new spending to rebuild schools and highways and avoid layoffs of teachers and other public employees.
Schumer said he might pair one element Republicans don't like -- an infrastructure bank to fund construction projects -- with a repartition measure that would allow multinational firms to bring earnings back to the United States tax-free, which is backed by Republican allies in the business community.
A group of business leaders led by GE chief executive Jeffrey Immelt delivered a report to Obama this week proposing steps to foster U.S. innovation and make the country more attractive to foreign investment. It was not clear if any of the ideas would be advanced by Democrats in the near term.