Columbus, Ohio (CNN) -- High school students chanted "pass this bill" to a rousing speech Tuesday by President Barack Obama touting his $447 billion jobs plan, while senior administration officials said the push for Congress to approve the legislation would last months.
White House spokesman Jay Carney, meanwhile, opened the door to Obama's proposal getting passed in pieces, rather than as a single package.
"If Congress were to send a portion of the American Jobs Act, the president would, of course, not veto it," Carney told reporters. "He would sign it and then he would return to press the Congress to get the rest of the job done."
The plan unveiled last week and presented to Congress on Monday calls for targeted tax cuts, infrastructure spending and new job training assistance that would be paid for by ending tax loopholes for corporations and American families earning more than $250,000 a year.
Congressional Republicans said Tuesday they were open to some aspects of the president's jobs plan, but they rejected Obama's proposal to pay for the measure with what they labeled tax increases.
"This proposal is really not credible," said Senate Minority Leader Mitch McConnell, R-Kentucky, while House Speaker John Boehner, R-Ohio, questioned the so-called "pay-for" provisions in the measure.
"We see permanent tax increases put into effect in order to pay for temporary spending," Boehner said. "I just don't think that's really going to help our economy the way it could."
House Majority Leader Eric Cantor, R-Virginia, indicated legislators can agree on expanded tax breaks for small businesses and rolling back some regulations.
However, House Republicans will oppose having the wealthy pay more in taxes to fund the jobs plan, he said.
"Republicans are not going to accept tax increases if the goal is to grow the economy," he said.
House Democratic Caucus Chairman John Larson of Connecticut, meanwhile, predicted that if Republicans "cherry pick" only the pieces of the plan they like, Congress would "find ourselves in the same kind of morass that we have in the past."
Democrats argued that the new spending on schools, roadways and airports the president wants, but the GOP is opposing, removes a centerpiece of the proposal that they believe will generate jobs.
"Every nation in the world that is our competitor is investing in infrastructure. The Republicans are suggesting disinvestment in infrastructure, cut infrastructure investment." Rep. Steny Hoyer of Maryland, the No. 2 House Democrat, said.
To Obama, the Republican opposition amounts to political obstinacy, and he encouraged a crowd of more than 3,000 students and others at the Fort Hayes Arts and Academic High School to telephone, email, tweet and fax their congressional representatives to support the jobs plan.
"They supported this stuff in the past, but they're saying maybe they don't do it this time because Obama's proposing it," he said. "It's not about giving me a win. ... It's about giving people in Ohio a win."
Senior administration officials said Obama would spend most of the rest of 2011 making his case for Congress to pass the jobs plan, including taking his message outside Washington as he did Tuesday.
In addition, Obama will schedule another bus tour like a recent three-state swing and target regional media outlets with advertisements, the administration officials said.
Carney said the idea is to ratchet up public pressure on Congress, particularly Republicans, to act on behalf of the nation rather than party interests.
"Congress will have a lot of explaining to do if, come the end of the year, they have done nothing to address Americans' number one priority," Carney said, later adding: "We live in a time when we have to make choices."
CNN's Tom Cohen, Deirdre Walsh and Ted Barrett, and CNNMoney's Jennifer Liberto contributed to this report.