Washington (CNN) -- President Barack Obama took the push for his stalled $447 billion jobs plan to North Carolina on Monday, telling two audiences that alternative proposals put forward by his Republican critics amount to little more than sops to the rich that will gut critical regulations and fail to restore economic growth.

My "bill will help put people back to work and give our economy a boost right away," Obama told a morning crowd at Asheville Regional Airport. "But apparently, none of this matters" to GOP leaders.

"I've gone out of my way to find areas of cooperation" with congressional Republicans, the president declared. "We're going to give members of Congress another chance to step up to the plate and do the right thing."

But "if they vote against these proposals again ... then they're not going to have to answer to me. They're going to have to answer to you," he said.

Later Monday, Obama told students at West Wilkes High School in Millers Creek that Republican opposition to his plan "makes no sense," and he criticized the GOP alternative proposal as an attempt to satisfy the party's conservative wing.

"It's way overdue for us to stop trying to satisfy some branch of the party and take some common-sense steps to help" the economy and the nation, he said to a cheering crowd.

Since Obama's plan was rejected in the Senate -- due to unanimous GOP opposition -- Democratic leaders have decided to try to move it through Congress by breaking it up into a series of smaller legislative proposals.

But his appearance, analysts note, was as much about campaign politics as the bill. The president will spend the next three days on a bus tour through politically pivotal North Carolina and Virginia -- two states carried by Obama in 2008 but considered up for grabs next year.

Veteran Sen. John McCain, R-Arizona, whom Obama defeated in the 2008 election, criticized the president Monday for using the taxpayer-funded trip for what McCain called political campaigning.

"On the taxpayer-paid dime, the president is now traveling, attacking the Republican plan," McCain said on the Senate floor. While noting Obama's right to level such criticism in a political venue, McCain added: "Is that appropriate on the taxpayer's dime, since it is clearly campaigning?"

In Asheville, the crowd repeatedly chanted "four more years" before and during Obama's remarks.

"I appreciate the 'four more years,' but right now, I'm thinking about the next 13 months," the president said. "We don't have time to wait. We've got a choice right now."

Obama's senior strategist, David Axelrod, vowed Sunday that every part of the bill will eventually have a vote.

"The American people support every single plank of that bill, and we're going to vote on every single one of them," Axelrod said on ABC's "This Week."

He would not say which part of the plan would come first.

Republicans will "get a vote on whether they believe we should protect tax breaks for small business owners and middle-class Americans, or whether we should protect tax breaks for millionaires and billionaires," Obama said in a written statement last Tuesday.

Meanwhile, demonstrators in Southern California said they'd gather Monday to protest the GOP's stance on the president's jobs bill. House Speaker John Boehner, R-Ohio, and California Reps. Dana Rohrabacher and Ed Royce will be together in the area for a fundraising event.

"Members of the Courage Campaign, teachers and health care workers will deliver a petition to Speaker Boehner signed by 25,000 Courage Campaign members ... demanding that he hold a vote on President Obama's American Jobs Act," a statement from the demonstrators said.

House Majority Leader Eric Cantor, R-Virginia, said over the weekend that there could be agreement on some elements.

"Let's work together. Let's find some of the things in his plan that we agree with, and let's go ahead and do that for the American people," he told "Fox News Sunday."

The past week was an indication that "we can come together," Cantor said, citing the passage of three trade bills.

Cantor did not make clear exactly where areas of agreement may be. But he cited the need to help small businesses find capital, unemployment insurance reform and infrastructure spending as broad ideas for which both sides have expressed support.

But "we're not going to be for tax increases on small businesses," Cantor said of the president's plan.

Republicans filibustered the Senate version of the president's jobs bill last week, though a handful of Democrats had said they would have opposed the measure if it had made it to the chamber's floor.

Among other things, Obama's overall blueprint includes an extension and expansion of the current payroll tax cut, an extension of jobless benefits, new tax credits for businesses that hire the long-term unemployed and additional money to help save and create jobs for teachers and first responders such as firefighters.

The largest measure in the package is the payroll tax cut, which comes at a projected cost of $265 billion. Employees normally pay 6.2% on their first $106,800 of wages into Social Security, but they are now paying only 4.2%. That break is set to expire at the end of December. Obama wants to cut the tax in half, to 3.1%.

Republicans previously embraced the cut, but have increasingly questioned its economic merit.

A second key measure -- estimated to cost roughly $44 billion -- is the extension of emergency jobless benefits to help the long-term unemployed. Lawmakers first expanded benefits to cover 99 weeks in 2009, and have since reauthorized the expansion five times.

Republicans are at particularly sharp odds with Democrats over how to pay for the plan. GOP leaders oppose a provision that would fund the measure through a 5.6% surtax on annual incomes over $1 million. Republicans have accused the president of engaging in so-called "class warfare," while Democrats say wealthier Americans need to share in the cost of fiscal responsibility.

On Monday, a Senate Democratic leadership aide told CNN that Democrats will seek a 0.5% surtax on annual incomes over $1 million to pay for the first individual component of Obama's broader jobs package.

That component of the larger jobs bill would provide $35 billion in aid to states to help preserve jobs for teachers and first responders, the White House and Senate Majority Leader Harry Reid's office said.

However, a top Senate Republican leadership aide immediately said that Republicans -- and some Democrats -- probably would not be willing to go along with a tax increase to pay for the measure.