As part of President Barack Obama’s annual effort to provoke Republicans and cheer up disheartened Democrats, the president touched on a theme that he has deployed effectively in the past that is designed to inflame tensions between the genders: The idea that women are systematically discriminated against in the workplace.

“Of course, nothing helps families make ends meet like higher wages. That’s why this Congress still needs to pass a law that makes sure a woman is paid the same as a man for doing the same work,” Obama said during his State of the Union address. “It’s 2015. It’s time.”

Of course, the notion propagated by this White House – that women earn 23 percent less than a man does for the same job – is a demonstrable myth. That has not stopped the president and his allies from disseminating that politically beneficial lie. The fact that Obama chose not to repeat the hopelessly inaccurate statistic that women make 77 cents for every dollar a man earns does last night, however, does indicate that the fact checkers are effectively shaming the administration into being a touch more truthful.

For years, it has been in the administration’s best interests to drop that statistic. By the administration’s own dubious calculations, the White House pays women less than their male counterparts in similar positions – a condition that persists long after it was first revealed by investigative reporters.

“The average female employee at the White House earns about $78,400, while the average male employee earns about $88,600,” CBS News reported in June of last year. “That’s a gap of 13 percent – the same percentage as 2009, when the average woman made about $72,700 and the average man earned about $82,000.”

“Women tend to hold more junior positions than men, and among White House leadership just 53 female officials make more than $100,000 compared to 87 males who do,” the report continued.

White House advisor Valerie Jarrett was confronted over this disparity, and the hypocrisy associated with the president’s regular hectoring of others for a sin in which he also indulges, by potential Republican presidential candidate Carly Fiorina on Wednesday in an appearance on MSNBC.

Fiorina noted that, not only are there already anti-discrimination laws on the books and if women are truly being discriminated against, they have a legal recourse. Moreover, she added, the president is not leading on the issue because he cannot even address the pay disparity in his own White House based on the administration’s problematic calculations.

“I’m also struck by the fact that the single greatest impediment to equal pay for equal work is the seniority system,” Fiorina continued, “which pays not on merit, not on performance, but on time and grade.”

“And who is it that supports the seniority system?” she asked. “Unions. Government bureaucracies. The vast majority of constituencies that the Democratic Party represents and who supports the Democratic Party.”

“In the White House, women do earn equal pay for equal work,” Jarrett replied unconvincingly. She went on to ignore Fiorina’s astute questions and touted the Lilly Ledbetter Fair Pay Act signed into law in 2009 as evidence of the administration’s commitment to eliminate gender discrimination. “There’s no good reason why Congress hasn’t passed the paycheck fairness act!” she exclaimed.

So, if you were hoping for a final Götterdämmerung over the issue of equal pay between these two powerful female voices, you were disappointed. It was, nevertheless, clarifying to watch Jarrett adopt an evasive posture when confronted by the White House’s own pay gap.