President Barack Obama speaks on his proposed American Jobs Act Sept.13, 2011 during a visit to the Fort Hayes Arts and Academic High School in Columbus, Ohio.

One day after sending his latest jobs plan to Congress, President Obama said Republicans' unwillingness to embrace it wholesale amounts to political "games" meant to undermine his bid for re-election.

"Yesterday, there were some Republicans quoted in Washington  saying that even if they agree with the proposals in the American Jobs Act they shouldn't pass it because it would give me a 'win,'" Obama told a crowd of 3,250 supporters at a rally outside a Columbus, Ohio, public high school.

"'Give me a win?'  This isn't about giving me a win," he said. "This isn't about giving Democrats or Republicans a win. It's about giving the American people a win. It's about giving Ohio a win. It's about your jobs and your lives and your futures and giving our kids a win."

Obama delivered the pitch for his $447 billion proposal, first rolled out in an address to Congress last week and taken on the road to Richmond, Va., telling the crowd it would put more money in consumers' pockets and create or save tens of thousands of jobs.  He said up to 14,000 teacher, firefighter and other first-responder jobs facing elimination could be saved in Ohio alone.

"Call and email and tweet and visit and tell your congressperson that the time for gridlock, the time for games is over," an animated Obama told the crowd.

Republicans, however, suggested Tuesday that it was Obama who was playing games.

"We all get the joke. He's in Virginia, Ohio and North Carolina. Doing what? Selling to the American people for his re-election effort," said Republican National Committee Chairman Reince Priebus on a conference call with reporters. "With this president it's all politics, all the time."

Obama's visit to Franklin County, which he carried with 59 percent of the vote in 2008, underscored the importance of Ohio for Obama's 2012 campaign.  Wednesday he heads to Raleigh-Durham, N.C.,  another 2012 battleground he narrowly carried four years ago,  to make a similar pitch for his plan.

"I just don't think that's really going to help our economy the way it could," House Speaker John Boehner, R-Ohio, told reporters before Obama spoke in Boehner's home state.

"As we get into this conversation with the president about how we help our economy, I hope he'll listen to our ideas," Boehner said, "and I hope that he'll work with us to find common ground to get our economy moving and create jobs again."

White House press secretary Jay Carney told reporters on Air Force One before the president's speech that the administration is open to piecemeal passage of its jobs plan if the package cannot win support as it  is.

"We believe Congress should act on the American Jobs Act right away. We believe that if Congress were to send a portion of the American Jobs Act, the president would, of course, not veto it. He would sign it.  And then he would return to press Congress to get the rest of the job done," Carney said.

"We understand how Congress works, and we look forward to Congress moving quickly," he said, "not because we tell them to or the president tells them to, but because the American people are demanding that they act."

One sign of the administration's optimism? The choice of music blared over loudspeakers at the conclusion of Obama's speech: Stevie Wonder's 1970 hit single "Signed, Sealed Delivered."

ABC News' Jon Garcia contributed to this report.