Update: Lois Lerner has been put on administrative leave. It's easier to put a federal worker on leave than to fire him or her outright. 

One thing Republicans and Democrats probably agree on: Lois Lerner should lose her job.

Lois Lerner listens during a House Oversight and Government Reform Committee hearing in Washington, D.C., U.S., on Wednesday, May 22, 2013. (Pete Marovich /Bloomberg)

The director of exempt organizations at the Internal Revenue Service was inaccurate, at best, in her explanations of how targeting of conservative groups began and when she found out about it. She went on to plead the Fifth rather than testify before Congress, a decision that is bad for both the Obama administration and the Internal Revenue Service.

So why is she still employed?

There are only two political appointees at the IRS. Everyone else is a civil servant, and Politico explains that it's hard (though not impossible) to fire federal workers. The appeals process could drag out for over a year. And it's acting IRS commissioner Daniel Werfel who will make the decisions, not the White House.

Obama could ask for Lerner to resign, just as he asked for and received then acting IRS Commissioner Stephen Miller's resignation.

In Wednesday's daily White House press briefing, White House spokesman Jay Carney told reporters he could not say how the president felt about Lerner's decision to plead the Fifth.  Nor would he say that the administration would like to see her gone. Instead, he suggested that any further staff changes at the IRS would come after Werfel completes a month-long review of what went wrong.

"I think it's important to find the facts before you hold people accountable," he said. "That's why the president through [Treasury] Secretary [Jack] Lew has instructed the new acting commissioner on the job today to institute a 30-day review."

But Obama likely doesn't want to set a precedent of calling for the dismissal of civil servants he doesn't have the power to remove. So even if both liberals and conservatives want it, there's reason why the White House has stayed quiet.