The purpose of President Obama's visit to the the University of Michigan on Friday was to promote the administration's new, and genuinely innovative, program for making college more affordable. But, along the way, Obama made a point about his own biography – and, implicitly, about Mitt Romney's:

Michelle and I can still remember how long it took us to pay back our student loans. ... Your President and your First Lady were in your shoes not that long ago. We didn’t come from wealthy families. The only reason that we were able to achieve what we were able to achieve was because we got a great education. That’s the only reason. And we could not have done that unless we lived in a country that made a commitment to opening up opportunity to all people.

You can expect to hear a lot more of this if, as seems likely, Romney becomes the Republican nominee. You can also expect Romney and his allies to get angry about it. They think critics who talk about Romney's wealth, even indirectly, are practicing the “politics of envy.” And they would have a point if the critics were simply trying to stoke resentment towards the wealthy. They'd also have the public on their side, according to my colleague Alec MacGillis.

But Obama was actually making an argument about policy on Friday. Specifically, he was making the case for strong public programs – not only as a safety net, for those who face financial difficulty, but also as a ladder of upward income mobility, for those who can’t move up on their own. Here was the crucial passage, which came just before the remarks about Obama’s student loans:

My grandfather got the chance to go to college because this country decided that every returning veteran of World War II should be able to afford it. My mother was able to raise two kids by herself because she was able to get grants and work her way through school. I am only standing here today because scholarships and student loans gave me a shot at a decent education.

As Greg Sargent has observed, this is the same argument that liberals like Elizabeth Warren have been making for a while now. And it is relevant because Romney has said repeatedly that he wants to gut those same programs, as a new report from the Center on Budget and Policy Priorities confirms.

In a major campaign promise that has drawn surprisingly little scrutiny, Romney has vowed to cap non-defense spending at 16 percent of gross domestic product – a goal that would, by his own admissions, require about $500 billion in cuts in 2016. A few weeks ago, I suggested that, based on preliminary calculations, that would lead to massive reductions in programs – with student financial assistance a likely target. (Remember, House Republicans have tried to cut that already.) The Center’s report confirms that:

Presidential candidate Mitt Romney's proposals to cap total spending, boost defense spending, cut taxes, and balance the budget would require extraordinarily large cuts in nondefense programs. If policymakers cut all nondefense programs by the same percentage, the cuts would measure 21 percent in 2016 and 36 percent in 2021. If policymakers exempted Social Security from the cuts and then cut all other nondefense programs by the same percentage, the cuts would rise to 30 percent in 2016 and 54 percent in 2021.

Romney's plans would be we worrisome even if he hadn't grown up wealthy. But Romney himself points to his life story as proof that the American economic system works – and would work even better if only the government would get out of the way. "What we have -- what -- what I was able to build, I built the old-fashioned way, by earning it, by working hard," Romney said during last week's Tampa debate, adding later, "the nature of America is individuals pursuing their dreams ... [they] don`t make everyone else poorer; they help make us all better off. And so I`m not going to apologize for success or apologize for free enterprise."

Romney should be proud of what he’s accomplished. His success in college, graduate school, and business are testimony to his work ethic as well as his natural talents. But Romney also benefited from the lottery of life – among other things, by being born into a family that could afford to provide him with the very best education at every step of the way.* He seems unaware of that fact and the possibility that others, born into less fortunate circumstances, might need some of the government programs he's promised to undermine.

* For what it's worth, I've e-mailed the Romney campaign, to inquire whether he ever took out significant loans to pay for tuition in college or graduate school. But this reference from page 58 of The Real Mitt Romney makes me doubt it:

George [Romney, Mitt's father] confided his anxiety about Mitt. "He said he was concerned about the time Mitt was spending traveling back to Michigan on the weekends," [Mitt friend Alan] Abbott recalled. George planned to "cut back" on Mitt's allowance in the hope that Mitt would spend more time on campus and his studies.