He also made a strong pitch for raising the minimum wage.
Speaking to a sympathetic crowd at the Town Hall Education Arts and Recreation Campus in Washington, at an event hosted by the left-leaning Center for American Progress, the president cited Pope Francis and Abraham Lincoln and said the country is in an inequality crisis. He noted that the top 10 percent take home one-half of all income -- up from one-third in the 1970s.
Coupled with that, Obama said, statistics showed it was harder for the poor to rise, no matter how hard they worked.
Pointing to what he called a "broken" healthcare system, Obama said, "That's why we fought for the Affordable Care Act, because [before the 2010 law] 14,000 Americans lost their insurance each and every day, and even more died because they had no health insurance at all."
As the act has been gradually implemented, the growth of healthcare costs is at its slowest rate in 50 years, the president said.
The act, commonly known as Obamacare, has ended insurance benefit caps and pre-existing condition obstacles, and resulted in reduced bankruptcy, fewer sick days and healthier kids.
"Those are the things that will help reduce inequality," he said.
Despite the botched rollout of the act's website, the "law is working to benefit millions of Americans right now ... this law is going to work and for the sake of our economic security it needs to work."
If House Speaker John Boehner, R-Ohio, still thinks he can repeal it, Obama said, he "might want to check with the more than 60,000 people in his home state who have [already] signed up."
Moreover, if Republicans have an alternative to the program that would do the same things, they should speak up, Obama said.
"You owe it to the American people to tells us what you are for, not just what you are against," he said.
The president called for raising the federal minimum wage from the current $7.25 an hour.
"People who work their tails off" are having trouble supporting their families at that rate, he said.
"It's well past the time to [increase] a minimum wage that in real terms is lower right now than when Harry Truman was in office."
Obama laid out what he called a "road map" for the remaining years of his administration.
-- "Relentlessly push a growth agenda."
-- Make "sure we empower more Americans with the skills and education they need," including preschool.
-- "Empowering our workers ... so unions have a level playing field," and enacting laws that protect women and other workers.
-- "We've got to revamp retirement," encouraging more private savings and shoring up Social Security.
If it were not for Social Security, Obama said, half of Americans would live in poverty. Before Medicare, he said, half of seniors had no form of health insurance.
Making the case for government action to address inequality, Obama said, "More than half of Americans at some point in their lives will experience poverty."