The Obama administration surely didn't think it was penalizing its core middle-class constituency when it proposed, earlier this month, to raise taxes on college savings accounts known as 529s. After all, a majority of those accounts are held by people earning more than $150,000 a year, and the administration was proposing the change to pay for expanding a tuition tax credit for families making less than that.

Yet as the backlash to the proposal demonstrated, the soaring cost of a college education makes even a six-figure income seem small, and the definition of "middle class" quite elastic. In a remarkably quick turnaround, the White House on Tuesday dropped the 529 plan just over a week after announcing it. In doing so, administration officials let it be known that not only had top Republicans protested the change, powerful Democrats like House Minority Leader Nancy Pelosi were urging the president to scrap it as well.

Where did the White House go wrong? For one, President Obama has spent most of his time in office campaigning to reduce college costs, increase federal aid, and encourage saving. (Conservatives have even dug up quotes from his economic advisers praising the very 529 tax break he was proposing to scale back.) So going after a program designed to incentivize college seemed incongruous.

And while the president has shown no qualms about taxing the 1 percent to help out the 99 percent, this policy was not a simple shift of money from the rich to the poor, but from the financially comfortable to the somewhat-less-comfortable. The hardest hit might be those in the top 5 percent of earners, who are certainly financially comfortable but who are not millionaires, and for whom college tuition without the benefit of generous financial aid remains a pricey proposition. (And like their wealthier friends in the 1 percent, they happen to be disproportionately active in politics, particularly when it comes to campaign contributions.)

An even bigger political problem for the administration was that it did not propose to limit the tax increase to those earning more than $150,000 or $200,000. So although wealthier families would have borne the brunt of the change, it would have affected anyone with a 529 account, including the very people around whom the entire Democratic agenda is centered. That allowed Republicans like Speaker John Boehner to argue that Obama should withdraw the plan "for the sake of middle-class families."

The immediate practical impact of Obama's reversal is nil; congressional Republicans had already swatted down his tax plan, and to scrap a single element of the proposal is akin to plucking a feather from a dead bird. But as Jonathan Weisman noted while breaking the news in The New York Times, the retreat is yet another ominous sign for the prospects of a bipartisan tax overhaul. Lawmakers in both parties say they want to simplify the tax code and cut rates for the middle class, but doing so without busting the budget requires the elimination of dozens of popular tax breaks like the 529 incentive. Obama was similarly burned earlier in his tenure when he proposed a cap on charitable deductions, as was a top Republican tax-writer, Representative Dave Camp, when he unveiled a plan last year that would have eliminated the state and local tax deduction, the first-time homebuyer tax credit, and many other loopholes backed by powerful lobbying interests.

As with the college savings accounts, those incentives benefit both the 1 percent and people who may look rich but who don't feel rich. It's a debate that last played out in 2012, when in a last-minute concession, the Obama administration agreed to a fiscal-cliff deal that raised taxes on families earning more than $450,000, rather than its initial proposed threshold of $250,000. Now that Democrats and Republicans are both talking about the middle class, they can start by figuring out what exactly that means.