Deputy Attorney General Rod Rosenstein didn't inform the White House Counsel until after the deed was done:
Rosenstein, who is overseeing the Russia investigation because Atty. Gen. Jeff Sessions recused himself, did not inform either the White House or Sessions about the decision until after he had signed the order appointing Mueller, according to a Justice Department spokesperson who spoke on condition of anonymity.
About half an hour before the order was made public, a Justice Department official informed White House Counsel Don McGahn. Trump spokesman Sean Spicer abruptly left a scheduled meeting with reporters as White House aides huddled to draft a response.
Rosenstein was already reported to be livid that he had been made a patsy by the White House. They made him the fall guy for Trump's firing of Comey, but Trump himself quickly unraveled that lie. Having been burned once, and probably getting more than a few side eyes from his colleagues at Main Justice, Rosenstein, a career civil servant, had to move quickly and independently of the White House.
Why?
Because Trump will appoint a new FBI Director and Rosenstein wanted to wall this investigation off from whomever that particular guy is. Rosenstein has now handed ownership of the whole business of Trump and Russia to Mueller who is certainly isn't going to be anybody's patsy. Including whomever ends up being the new FBI Director. Rosenstein doesn't want to be made a fool of again and by doing it this way he can turn his attention back to routine law enforcement, anti-terrorism and counter-intelligence. Or cracking down on weed for some dumb ass reason as his boss Attorney General Jeff Sessions wishes.
For the White House, three things:
1. Lawyer up! Rest assured, at some point almost everyone including Donald Trump and Mike Pence, will be deposed under oath. If there is lying to the FBI, it will be prosecuted. If there is any hint of obstruction, it will be prosecuted.
2. The pardon power is the president's most sweeping and unchecked authority. This is a card Trump can play with his underlings who could face prison and/or a Himalayan scale of legal expenses. But he only gets to use it if he keeps the office. So expect them to fight it out somehow. However, they have to believe Trump will actually use the pardon. If they don't trust him, they'll turn. However, it should be noted that the office of Manhattan District Attorney Cyrus Vance, Jr. is also looking into Paul Manafort in his own criminal inquiry. Vance has state jurisdiction over Trump Tower and there nothing anybody can do about him as he is directly elected by Manhattan residents. Presidents cannot issue pardons for state crimes.
3. Watch for Trump to possibly set up his own commission to look into Trump Russia like Reagan did during Iran Contra. While the prosecutor in that scandal was able to indict a bunch of Reagans officials, the Tower Commission was able to keep Reagan protected. Better to be incompetent than criminal. Trump won't like either, but forced to choose he will take the former.
For Democrats in Congress there is a formula for what to do with these things. Work hard at every public hearing you can get and you keep Trump Russia in the news. The proverbial 'cloud over the White House' strategy. With Trump's penchant for cable news consumption, a weird habit if you ask me, that is going to make him go berserk. Opportunities to capitalize abound.
Finally, I'd just like to say that I marvel at the wisdom of our Founding Fathers during times like this. By setting up a system, however imperfect, of power diffused widely both within government and even moreso throughout a vast array of private and civic institutions, they built a form of self-government that could withstand the sorts of shocks that have destroyed other republics since ancient times. They made our president just strong enough to allow a stupid mob to blow off steam, but not too strong to destroy what they so carefully built. Once again, our Constitution, however imperfect, will save the day.