In a series of tweets, Trump called the appointment of a special prosecutor "the single greatest witch hunt of a politician in American history!"
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As news broke Wednesday that deputy attorney general Rod Rosenstein had named Mueller, a former FBI director, as special prosecutor, Trump was curiously quiet on social media, where he typically expresses his frank outrage.
The fact that Mueller's appointment has garnered near-universal praise has probably made it more difficult for Trump and the White House to oppose his oversight over the investigation.
The Lawfare blog, one of the preeminent sources for legal news, hailed Rosenstein for naming Mueller the special prosecutor.
"There’s a lot of reason to be cheered this evening by the decision of Deputy Attorney General Rod Rosenstein to name a special counsel to investigate L’Affaire Russe, and there’s even more reason to be cheered that the individual he selected is Robert Mueller," Lawfare staff wrote Wednesday.
Lawfare noted that Mueller is of "sufficient stature" that if Trump tried to interfere in the investigation in anyway there would be an immediate scandal.
For Trump, the naming of a special prosecutor was not the most intrusive development as far as the Russia-election investigations are concerned.
Democrats are still calling for an independent commission, similar to the one created in the aftermath of Sept. 11, to buttress the probes being carried out by the FBI and various committees in Congress.
GOP congressman, however, have been determined to stop any more investigations from taking shape. House Republicans voted Wednesday to block legislation that would have created an independent commission to investigate Russian interference in the 2016 election.