(CNN) At 6 p.m. ET Wednesday night, Republicans breathed a big sigh of relief.

Deputy Attorney General Rod Rosenstein announced that he had decided to appoint Robert Mueller as a special counsel to oversee the ongoing federal probe into Russia's attempts to influence the 2016 election and any possible collusion between the Russians and the Trump campaign.

Bringing in an independent investigator was the best possible option for Republicans, as many acknowledged in private, hoping to find a way beyond the chaos caused by the investigation and Trump's response to it.

If Mueller found no proof of wrongdoing, Trump -- and the broader GOP -- would have a non-partisan stamp on their claims that there really wasn't anything to see here. If, on the other hand, Mueller found wrongdoing, the Trump Administration would be forced to deal with it and the chips would fall where they may. Sure, the broader GOP might suffer some political blowback from such an outcome but at least it would all be over -- and Republicans could begin to move on.

That relief held until just before 8 a.m. ET Thursday when Trump, who had been noticeably silent on Twitter over the past 24 hours , picked up his phone again.

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