All that said, I disagree with Patashnik's suggestion that, once in office, Obama would prioritize education more than Clinton would. That could be true, but there's not a lot of evidence for it from where we stand. Neither Obama nor Clinton has injected education into the race in a deeper way than occasionally criticizing No Child Left Behind and promising to overhaul it. Supporting new ideas in white papers doesn't necessarily equal a commitment to pushing them through Congress.
In terms of pushing things through congress, I'd say the most important factor is this. Ted Kennedy and George Miller chair, respectively, the Senate and House education committees. They're the main Democratic architects of No Child Left Behind, and they're both supporting Barack Obama. Hillary Clinton, by contrast, has gotten a lot of support from the American Federation of Teachers which has been generally hostile to the broad thrust of what Kennedy and Miller have been doing. So while it's far from clear that either would-be president would, in practice, do anything noteworthy on K-12 education, an Obama administration would create a situation in which all the White House and the main legislative players regard each other as allies.