(CNN) America may soon have yet another acting Cabinet official, as Labor Secretary Alex Acosta hangs by a thread over his links to a 2008 plea agreement for Jeffrey Epstein .

Acosta, who as a US attorney in Miami signed off on what critics now say was a lenient non-prosecution agreement with the hedge fund manager, has become a liability for his boss in an episode that is casting a questionable light on some of President Donald Trump's own decision making.

More than a decade on from Acosta's involvement in the case, Epstein's arrest in New York and indictment on charges of sex trafficking and child sexual abuse in Florida and his Manhattan home between 2002 and 2005 have reignited claims that Acosta breached public trust and is unfit for federal office.

Epstein has pleaded not guilty to the charges.

The suddenly hot issue not only is forcing Trump to address Acosta's actions,the case itself -- with its horrific allegations -- and his own decision to nominate the labor secretary, but is also reminding Americans that Epstein was once one of the President's own high-living friends. Trump is not the only top politician who is being asked what he knew about Epstein's behavior; former President Bill Clinton also traveled on themultimillionaire's plane.

If the past is a guide, Acosta's fate will not be sealed by the President's defense of him Tuesday but by how media coverage plays out in the coming days and how Trump's army of informal on-the-phone advisers think the furor is reflecting on him.

While Trump has told people he has confidence in Acosta, speculation about the labor secretary's fate will likely rise after Trump's friend Christopher Ruddy, the CEO of Newsmax, told Don Lemon on "CNN Tonight" Tuesday that he thought Acosta will not be in his post much longer.

"I think the plea agreement he did is indefensible. I think that he is not going to stay for long," Ruddy said, though he cautioned that he had not spoken to the President about Acosta.

Acosta responded to the rising storm by defending himself on Tuesday, saying his actions had resulted in Epstein going to jail -- for 13 months of an 18-month sentence -- registering as a sex offender and putting the world on notice that he was a sexual predator.

"Now that new evidence and additional testimony is available, the NY prosecution offers an important opportunity to more fully bring him to justice," Acosta tweeted.

Given the lurid allegations against Epstein and the prospect of months of revelations that may look bad for Acosta, the President may just decide he doesn't need the headache. The process could take weeks or months to play out, though, since canning Acosta could be seen as Trump caving to critics and an admission that he had been wrong to nominate Acosta in the first place.

The episode is also exposing some of the less appealing traits of Trump's presidency. They include thin vetting of some Cabinet officers as well as Trump's apparent inclination to give the first benefit of the doubt to some men directly or indirectly caught up in dramas involving allegations of sexual misconduct against women.

The Epstein case is also a reminder of how rich and politically connected men seem to have evaded scrutiny and justice when faced with allegations of sexual misconduct -- until now, a societal shift the President has seemed slow to embrace.

Trump -- who has denied claims of sexual assault himself -- often seems to instinctively side against the accusers in such cases, as with allegations against his Supreme Court nominee Brett Kavanaugh or Roy Moore during the former judge's previous US Senate run in 2017 in Alabama. Such equivocation may hurt Trump politically with the moderate and female voters who could be important to deciding the 2020 election.

Another sign that Acosta is on thin ice is the zeal with which Democrats have started to attack him as a way of questioning Trump's judgment, morals and management skills. And GOP lawmakers are having to dodge and weave in the corridors of Capitol Hill, unwilling to cross the President on an issue that weighs on his decisions or acumen.

Trump feels 'badly' for Acosta

Trump was forced Tuesday into one of his ritualistic defenses of Cabinet secretaries under fire.

"I can tell you that for two-and-a-half years he's been just an excellent secretary of labor, he's done a fantastic job," Trump said, seeking to dilute Acosta's responsibility for the non-prosecution agreement, under which Epstein pleaded guilty to two state charges of soliciting prosecution, including with a minor.

"I do hear that there were a lot of people involved in that decision. Not just him," Trump said.

But as with many of the President's public votes of confidence, he left himself sufficient wiggle room to suggest Acosta might be advised to polish up his resume in any case.

"The rest, we'll have to look at it, we'll have to look at it very carefully," Trump said, referring to Acosta's role in the Epstein saga.

The President did say he felt "very badly" for his labor secretary but that may not be much consolation, since he has previously used similar verbiage about other associates who faced criticism -- including jailed ex-campaign chairman Paul Manafort and his forme r national security adviser Michael Flynn.

Trump, despite his reality TV show catchphrase "You're fired," often seems to vacillate over the squeamish job of dismissing Cabinet secretaries. But over time, his implied lukewarm support and noncommittal comments create an impression that they have lost presidential support -- which leaves their positions untenable.

A more traditional president might worry about the chances of confirming a replacement for Acosta given the quickening campaign calendar, which will soon jam up Washington politics.

But Trump has shown little such concern. In fact, he has indicated he likes having acting secretaries in place because it gives him more leverage and power.

Lawmakers respond

With the evidence available more than a decade ago, federal prosecutors insisted that Epstein go to jail, register as a sex offender and put the world on notice that he was a sexual predator. — Secretary Acosta (@SecretaryAcosta) July 9, 2019

Some lawmakers say decisions on Acosta's fate should await Justice Department inquiries and should rest only on a fair assessment of his actions in Miami.

But politicians in Washington have an animal sensitivity when a weakening member of a rival herd may be nearly ready to be picked off. So Democrats jumped at the chance to renew their attacks on Acosta -- aiming reflected fire at Trump.

House Speaker Nancy Pelosi suggested that the President was aware all along of the questionable plea deal for Epstein approved by Acosta -- and didn't care.

"He knew about this when he nominated him for the Cabinet. It just goes to show you," the California Democrat said.

Democratic presidential front-runner Joe Biden used the moment to demand Acosta's resignation, indirectly bolstering his top campaign asset -- that he's seen as best equipped to take on Trump.

"The abuse of a child is one of the most heinous, despicable abuses of power imaginable," Biden tweeted. "It is inexcusably poor judgment for a US Attorney to seek leniency for someone guilty of it."

Republicans were forced into their familiar dance of being asked to comment on unflattering stories about the administration.

Senate Majority Leader Mitch McConnell, a Kentucky Republican, punted by saying it was up to the President to decide the fate of his appointees. House Minority Leader Kevin McCarthy, a California Republican, professed ignorance of the case and its implications: "I don't know enough about it to say," he said.

Sen. Ben Sasse of Nebraska has repeatedly called for a reexamination of the Epstein plea deal but was not willing to say Tuesday whether the labor secretary should resign. He said he wanted to wait for the outcome of a Justice Department inquiry, which he forced, before talking about individuals.