As he has barnstormed the country to promote the American Jobs Act, President Obama has made the case that spending money now will pay off later for the United States’ global productivity and competitiveness. And one of the biggest investments he is proposing comes in education.

Obama’s $447 billion jobs package includes $30 billion to renovate high schools and community colleges nationwide, and an additional $30 billion to help local jurisdictions hire and retain teachers.

On Tuesday, Obama wrapped up a three-day, three-state western swing by rallying students and teachers at Abraham Lincoln High School in Denver, his latest method of highlighting the education proposals and putting public pressure on congressional Republicans to support the jobs bill.

“Places like South Korea are adding teachers in droves to prepare their kids for the global economy. We’re laying ours off left and right,” Obama told students and teachers in the school’s parking lot. “All across the country, budget cuts are forcing superintendents to make choices they don’t want to make. . . . It’s unfair to our kids; it undermines their future; it has to stop.”

The stimulus bill comes as the administration is also aiming to reduce the federal deficit by an additional $3 trillion over the coming decade. To help pay for the jobs package, the White House has proposed eliminating many tax loopholes and write-offs for individuals earning more than $200,000 and families earning more than $250,000.

The “spend now” argument is crucial to Obama’s philosophy that the federal government cannot simply cut spending and expect to recover quickly from the economic slowdown and reduce the high unemployment rate. He has insisted on a “balanced approach,” a mix of tax cuts for small businesses and investments in schools and roads.

But while Republicans have agreed with the president on the tax breaks, they have pushed back on the idea that new spending will help solve the nation’s problems.

House Speaker John A. Boehner (Ohio) argued that Obama already tried this approach, unsuccessfully, with his $814 billion stimulus two years ago.

“The 2009 stimulus bill included $53.6 billion in state stabilization funds under the guise of preventing the layoff of teachers, law enforcement officers, and other municipal employees,” Boehner wrote in a recent memo to fellow House Republicans. “This band-aid approach masked over the true fiscal problems facing states and local governments. Some jurisdictions used the funds to provide one-time raises; others retained employees for a short-period of time, only to lay them off later. The President is proposing more of the same with an additional $30 billion in spending.”

The White House said Obama’s schools proposal would help save the jobs of as many as 280,000 teachers and modernize up to 35,000 schools nationwide, adding computer labs and replacing aging roofs and boilers.

Under the plan, 40 percent of the $30 billion for renovations would go to the 100 school systems with the largest numbers of low-income students; the other 60 percent would be given to states to allocate among high-need districts, including those in rural areas.

A chart released by the White House shows that D.C. public schools would receive $85 million in modernization funds, which could support 1,100 jobs. Maryland would receive $316 million (4,100 jobs), and Virginia would get $425 million (5,500). All three jurisdictions also would receive additional money to support community colleges.

States would have three to six months to get the money to the school districts, which would have two years to spend it on modernization projects, the White House said.

White House press secretary Jay Carney struck back at Boehner’s contention that the 2009 stimulus did not help save public-sector jobs, arguing that the injection of money helped keep teachers on payrolls. He added that more money is needed now that economic data show growth in the private sector alongside public-sector layoffs caused by steep cutbacks in state and local budgets.

“The job losses that we’ve seen this year have been in the public sector, and those cuts have been teachers,” Carney said. “If [Republicans] are saying it’s not a problem that states are shedding teachers from our payrolls . . . then they should say so.”

After Obama finished his remarks at the high school, Shelley Fryer, 57, an unemployed teacher from Denver, shouted to Carney, asking him to help her get a job. “Pass this bill,” Carney replied, referring to Congress.

In an interview, Fryer said she moved to Denver in 2008 from Los Angeles because her husband was worried about California’s budget crisis. But since moving, Fryer said, she has been unable to find work as a 12th-grade social studies teacher, even though she has a teaching license and a doctorate.

She said she supports Obama and thinks his rivals in Congress are obstructing his agenda to improve their own election chances.

“I’m the best teacher you’re ever going to see, and I can’t get a job,” Fryer said, trying unsuccessfully to hold back tears. “I just want to go back to work.”