Following President Obama's NBC interview in which he said his aides were looking into ways to provide some sort of relief for millions of Americans with cancelled insurance policies, the Huffington Post's Sam Stein reported that officials are considering an "administrative fix" for those whose insurance premiums are going up, but who earn too much to qualify for federal subsidies.

It's hard to imagine what such a fix would be, as anything that would adjust the formula for calculating subsidies would require an act of Congress.

But given that the administration has found various ways to re-write the law (such as delaying the enforcement of the employer mandate and weakening income verification measures), it's worth examining further, especially because Stein is well-sourced within the Obama White House.

Stein writes that, "According to the administration source, the White House is 'looking at an administrative fix for the population of people in the individual market who may have an increase in premiums, but don’t get subsidies.'”

Right now, subsidies for individuals to purchase insurance through an exchange top off at 400 percent of the federal poverty level, which is the equivalent of an individual earning about $46,000.

According to Stein, the theoretical administrative fix would seek to address those who don't qualify.

Beyond the legality of such a "fix," it would drive up the price of Obamacare substantially, given that the exchange subsidies are the costliest aspect of the law.

And past cost estimates from the Congressional Budget Office show us just how expensive changes to the subsidy formula might be.

In June 2009, the CBO evaluated a draft proposal from the Senate Health Education Labor and Pensions Committee that offered subsidies as high as 500 percent of the federal poverty level.

In the period from 2014 through 2019 alone, CBO estimated that the exchange subsidies would cost $1.2 trillion.

At the time — Obama signed the final legislation the following March, with the less generous subsidies — CBO estimated they would cost $458 billion over the same six-year period.

Sure, in theory, any "fix" to subsidies could be more targeted and might not raise costs quite this much. But still, this provides an idea of how costly it can be to play around with subsidies, especially if they are adjusted enough to substantially mitigate the problem of "sticker shock."

Thus, even if administration officials find a magic way to increase subsidies without Congress, Obama will be forced to answer for another famous pledge:

"I will not sign a plan that adds one dime to our deficits — either now or in the future. I will not sign it if it adds one dime to the deficit, now or in the future, period."