WASHINGTON (Reuters) - President Barack Obama urged Republicans on Saturday to stop picking "ideological fights" and focus instead on job creation efforts as he pressed Congress to begin voting next week piece by piece on his defeated jobs package. With an eye to the 2012 election, Obama is working with fellow Democrats to break into parts his $447 billion jobs bill -- which Republicans blocked in the Senate on Tuesday -- and challenge their opponents to show where they stand. He used his weekly radio speech to showcase his strategy to paint the Republicans as obstructionists impeding his drive to improve the economy and reduce stubbornly high unemployment, considered crucial to his re-election prospects. Republicans have said Obama's original package was laden with what they see as wasteful spending and counterproductive tax hikes for wealthier Americans and that he now seems more interested in demonizing them than working to find common ground. The deadlock on jobs has raised concerns that political dysfunction in Washington may make it impossible to take major steps to spur hiring before next year's presidential and congressional elections. "Republicans (in the House of Representatives) spent the past couple days picking partisan ideological fights," Obama said, citing Republican proposals over the past week to ease environmental regulations and restrict abortion funding. But Obama, who has adopted an increasingly populist tone in the jobs debate even as his poll numbers have languished, said he would give Republicans "another chance to spend more time worrying about your jobs than keeping theirs." "Next week, I'm urging members of Congress to vote on putting hundreds of thousands of teachers back in the classroom, cops back on the streets and firefighters back on the job," he said, identifying the first piecemeal proposal he wants lawmakers to bring up. "And if they vote 'no'" on that, they'll have to tell you why." Obama was referring to a portion of his jobs package that is seen having little chance of winning Republican support -- giving billions of dollars in aid to states to prevent layoffs of teachers and support the hiring of police and firefighters. POLL SHOWS SUPPORT FOR OBAMA PLAN A Wall Street-NBC poll this week showed the public, by a 2-to-1 margin, backed Obama's jobs plan through a mixture of stimulus spending and tax cuts. Democratic leaders propose financing it with a 5.7 percent surtax on millionaires. Senate Republicans offered a largely repackaged plan of their own on Thursday that featured calls for tax reform and cuts plus repeal of Obama's U.S. healthcare overhaul and lifting prohibitions on offshore energy exploration. Republicans, who control the House of Representatives, have in the past backed some components of Obama's package, such as a payroll tax cut, but have suggested they may not do so again. Obama said he wanted other elements of his plan put to a vote in coming weeks, including infrastructure spending, small-business tax breaks, preventing middle-class tax hikes from kicking in next year and extending unemployment aid. Obama, who has spent the past month barnstorming across the country touting his jobs package, will make a bus tour from Monday to Wednesday through North Carolina and Virginia, two election battleground states.