(CNN) What seemed at first like a long-awaited opening to get rid of the "lingering stench" at his Justice Department now poses a quandary for President Donald Trump: Would firing Deputy Attorney General Rod Rosenstein complicate precarious confirmation proceedings for an embattled Supreme Court nominee?

It would, according to Republican allies of the President, who have urged him to hold off on a purge of Justice Department officials until Brett Kavanaugh is safely in place on the high court. For now, Trump appears to have listened, though he has made clear his desire to rid the agency of officials he has deemed disloyal and corrupt.

In the immediate hours after The New York Times reported Friday on Rosenstein's supposedly sarcastic musings about wearing a wire to document chaos in the administration , Trump questioned whether to fire him immediately, people familiar with the conversations said. Some of his staunchest allies seemed to goad him to do it. Fox News hosts Laura Ingraham and Jeanine Pirro posted messages on Twitter declaring Rosenstein must swiftly be dismissed.

But in Washington, more cautious voices warned of outcry on Capitol Hill if Trump moved to fire the man who oversees special counsel Robert Mueller's Russia investigation. The fallout could muddle efforts to get Kavanaugh confirmed, Trump's allies warned, particularly as some senators are wavering in their support amid the sexual assault claims against the nominee, which the judge has denied. Ingraham — who'd earlier declared on Twitter "He needs to go. Today" — deleted her tweets.

The dynamic reflects the lingering anxiety among White House officials and establishment Republicans over Kavanaugh's prospects in the Senate, where the allegations have thrown a once-certain confirmation into question.

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