Job listings sometimes tell the unemployed not to apply at all (some states have toyed with legislation to prevent this).

For others, it's simply understood that the resumes of unemployed people will be tossed in the trash first. In a competitive job market, it's a quick way to weed out applicants.

Not only is this discriminatory, said Maurice Emsellem, policy co-director at the National Employment Law Project, an advocacy group. "It's not in the interest of employers to artificially limit the applicant pool."

'I want to go back to school'

"That gentleman in the back -- with the pink tie," Peters said, looking at House Speaker John Boehner, who was seated behind the president on the television. "He's always so angry! Gosh! He can't stand that president. Look at his attitude!"

Peters blamed Boehner's apparent lack of interest for holding back Obama's more aggressive attempts to push through job-creating reforms.

Boehner leaned to one side, almost out of the frame. He did look pretty bored as Obama argued that America needs to bring in new-era manufacturing jobs and invest in technologies to fight climate change and promote clean energy.

Peters said she felt unprepared for most of those jobs, anyway. She finished high school in New York and went to college for one semester before dropping out, she said, for financial reasons. After she was laid off in 2008, she told me, she became certified to work as an administrative assistant in a medical office. She never was able to use that certification because she never could find a company to hire her to use those skills.

She has some gaps in her resume, but told me she was employed fairly steadily until the recession hit. While she used to be able to choose among jobs, now she can't find any.

Her financial troubles may hurt her kids' opportunities, too.

As Obama turned to the topic of new investment in schools, so that all kids will have an equal shot at a great education, Peters said this to me:

"Every parent's dream is to send their kid to college, and now it's like, 'Is it worth it?' Why send 'em to college? They won't be able to get a job after it."

She questioned whether she could afford school for her 7-year-old.

And Peters' other daughter, who is 19, dropped out of high school and hasn't earned a GED diploma, she said, in part because they can't afford to pay the test fees.

'Work together'

This sort of long-term hopelessness has the potential to truly change our nation. In the same way Great Depression thinking lingered long after the 1930s, the sense that things aren't going to get better could stick with people like Peters and her kids.

"The American worker is very pessimistic about the future," said Carl Van Horn, a professor at Rutgers who worked on a recent survey on the topic. "Only 19% (of people surveyed) said they thought the next generation would do better than theirs. That's a very, very depressing number, if you think about it. That's not a typical American viewpoint. Talk about American exceptionalism ... -- that's the opposite of it. "

Plenty of things have been suggested to help get the long-term unemployed back into the workforce again. The trick is figuring out what would be effective.

It seems each policy solution comes with additional problems.

Laws aimed at preventing discrimination against unemployed people could backfire. Job training programs might not provide the right skills. Investing in a new stimulus package, including federal contracts to build roads and such, might end with employed people being rehired, said James Sherk, a senior policy analyst at the Heritage Foundation. Giving tax breaks to employers who hire the long-term unemployed seems smart to me, but Gary Burtless, a senior fellow at the Brookings Institution, writes that some employers may be turned off by the extra paperwork.

Extending unemployment insurance is a political nonstarter. A raised minimum wage, which Obama proposed on Tuesday, helps only if you're working.

What the problem really comes down to, Peters told me, is ignorance.

Most people don't know what it's like to be unemployed for months or years. If they understood, they'd be slower to toss the resume of an unemployed person.

And Congress could use a little education.

"How are the American people going to get back to work," she asked, "if we all don't work together?"