Paul Krugman points out the declining value of Pell grants and the impact that it has had on college education for lower income students. He writes: "Next time someone tells you that he’s in favor of equality of opportunity, not equality of results, ask him whether he proposes to reverse the decline in Pell grants and other programs giving educational opportunity to the less fortunate. If he demurs, he’s a hypocrite."
The fact is, this distinction between "equality of opportunity" and "equality of results" is pretty meaningless. What kind of "equality of opportunity" is really in play if kids growing up with less opportunity to fulfill their potential fail to achieve at a level that will get them into college - say, on a scholarship. Equality of opportunity and equality or results are inextricably linked. Unequal results of earlier generations (whether "legitimate" or not) produce unequal opportunities for future generations. If you obsess over the "deserving poor" and ideas like that, you're going to fail to guarantee equality of opportunity.
Buttressing Pell grants is a good idea, but another good idea that Krugman doesn't mention here is improving middle-skill educational opportunities that are weaker in the United States, like career and technical education and apprenticeships. But that's just one piece of the puzzle - ensuring access to college is critical.