If there was any remaining doubt that President Trump blundered badly by impulsively firing FBI Director James Comey, it ended on Wednesday. Deputy Attorney General Rod Rosenstein announced that former FBI Director Robert Mueller would be appointed as a special counsel to investigate potential links between the Trump campaign and Russian officials who attempted to affect the outcome of the 2016 elections. Even if Mueller's investigation does not result in Trump being removed from office, it's a big deal that is likely to change the political dynamics under the Trump administration.
The widely respected Muller is not going to be a patsy for the Trump administration, and the fact that he will be resigning from the prestigious law firm WilmerHale makes it clear that he's in it for the long haul. While his investigation will have a wide latitude on a day-to-day basis, Mueller is not a truly independent counsel and formally serves at the pleasure of the Department of Justice (and therefore, ultimately, the president), but as Trump has learned the hard way, firing Mueller would have the political effect of a guilty plea.
Particularly given the recent news that Trump nominated Michael Flynn as his national security adviser while knowing he was under federal investigation, it seems likely at a minimum that Mueller's investigation will uncover embarrassing information, and very possibly criminal activity, by people involved with the Trump campaign. And given Trump's recklessness and less-than-firm adherence to rules and norms, Mueller may uncover worse than that.
We have no way of knowing at this point, of course, what Mueller will find. But history can provide a couple of scenarios for thinking about how this investigation might play out.
The most common analogy will be Watergate, and the evidence that Trump committed obstruction of justice will only make the comparisons more common, given that this offense is exactly what did Nixon in. It is possible that Mueller will find something so damaging that Trump will be forced to resign or the necessary bipartisan supermajority in the Senate would plausibly convict him if he was impeached by a majority of the House.
Possible, but probably quite unlikely. Nixon's resignation occurred in a very different political context. Not only did the Democratic Party control Congress, but the Republican Party had a much larger moderate wing than it does today. It is highly unlikely that President Nixon would have been forced out of office if he was working with today's Congress. Mueller might find something so damaging that congressional Republicans conclude that it's in their interests to abandon Trump. But I strongly doubt that confirmation of the obstruction of justice, which Trump all but admitted to already, would be sufficient.
As Washington Post political reporter David Weigel shrewdly observed, a comparison that is likely to be more apt is the Reagan administration's Iran-Contra scandal. The discovery that officials within the administration had facilitated the sale of arms to Iran partly in order to illegally fund the Contra rebels in Nicaragua and partly to secure the freedom of some hostages was a substantial embarrassment, and lower-level officials were implicated in illegal activity. But it was never proven that Reagan himself was involved, and he was never seriously threatened with impeachment. With partisan polarization having intensified, this is probably the more likely scenario even if Trump's actions turn out to be more like Nixon's than Reagan's.
Iran-Contra didn't lead to Reagan's removal, but that doesn't mean it didn't matter. Reagan's approval rating dropped by roughly 20 points after the illegal arms deal was revealed. This caused the Reagan administration to pivot in a more moderate direction. Most notably, the collapse of Reagan's popularity helped contribute to the defeat of Reagan's Supreme Court nominee Robert Bork, which in turn almost certainly saved Roe v. Wade from being overruled.
Even if Trump survives Mueller's investigation, then, it is still likely to hobble his administration politically. His already-weak approval ratings are more likely to get worse than better. This will make it harder for Republicans to retain the House in the 2018 midterms, and will also hobble the passage of the party's already unpopular legislative agenda. Indeed, we may look back and conclude that Trump's decision to fire Comey saved 24 million people from having their health insurance taken away.
The Meuller investigation, in short, is bad news for an already tottering administration. The only question is how bad it will prove to be.