Julian Zelizer, a history and public affairs professor at Princeton University and a CNN political analyst, is the author of " The Fierce Urgency of Now: Lyndon Johnson, Congress, and the Battle for the Great Society. " He's co-host of the "Politics & Polls" podcast. The opinions expressed in this commentary are his own.

(CNN) In seven tumultuous days President Trump went from focusing on how the Senate would handle health care and tax cuts -- and preparing for his first trip overseas -- to learning he would face a special counsel, Robert Mueller, investigating contacts between Trump campaign aides and Russia. By the end of the week, some were even discussing the possibility of impeachment.

As if this were not enough, as the President left the country Friday the New York Times published a bombshell story about Trump's infamous recent meeting with Russian officials -- the day after he fired FBI director James Comey -- during which he allegedly told his visitors, "I just fired the head of the F.B.I. He was crazy, a real nut job. I faced great pressure because off Russia. That's taken off."

Trump also said, "I'm not under investigation," according to the Times, citing notes that were taken on the meeting.

Although legal experts filled the airwaves discussing the implications, the truth is that much of what happens next will depend on how the politics unfold. The fate of presidents who face scandal is largely determined in a political arena rather than a court of law. Surviving a scandal of this proportion requires immense political skills from the White House and a bit of good old-fashioned luck.

All eyes on Mueller

So what to look for in the months ahead?

The point man in the process will be Robert Mueller, who was appointed last week by Deputy Attorney General Rod Rosenstein. The Justice Department has given him broad discretion to look into what happened with Russia in the 2016 election and all related matters, including why the President abruptly fired Comey (who Mueller worked closely with under President George W. Bush).

The evidence that Mueller accumulates, and his ability to obtain strong testimony, will be the most central measure of his success. According to NBC News , the investigation is already looking into possible financial ties between Russia and another unnamed White House official.

But this job will also require political acumen from Mueller. He faces a hostile President who has already gone on social media to attack him and paint him as the lead figure in a partisan "witch hunt" of historic proportions.

Independent prosecutors, such as Lawrence Walsh and Kenneth Starr, learned how such attacks can damage perceptions of the integrity of the investigation. Mueller will need to keep this investigation focused and he will have to push back against any efforts to subvert his standing, because at some point he is likely to face an effort by the President to stop him or even fire him.

Already there are some analysts who claim that Mueller has a conflict of interest and should resign because his Washington firm represents Paul Manafort and Jared Kushner. Others argue that since Mueller didn't work on their cases, there is no problem.

Why legislation still matters

Even with the authority of the special counsel, Congress still has an important part to play, especially if Republicans finally start participating in the investigation rather than stalling and protecting Trump. Congressional hearings can be an important forum. Unlike Mueller's work, these can be conducted in public.

As President Nixon learned during the Watergate scandal, that kind of exposure can have a damning effect. If members are able to persuade administration officials to speak about what's happened, such testimony can sway the views of Americans watching.

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In the Senate, just a few Republicans would be necessary to turn the majority against Trump. There is not much the President can do to make them feel better, because he will never change his tune. But he can push for attractive legislation.

As legislators become more focused on the 2018 midterm elections and the 2020 presidential election, what they need most to re-energize the Republican party is big-ticket legislation. If the White House can get its act together and start moving legislation on the Hill, that could just be enough to bolster his partisan support at a moment it is clearly faltering.

Legislation still matters to the temperature on Capitol Hill. The most dangerous development of the past week had to do with Republicans who have started to openly express their concerns about the administration. Hearing criticism from Republican leaders like Senator John McCain, who recently compared the Russia investigation to Watergate, changes the political dynamics of the investigation since it creates the possibility of bipartisan opposition.

There is also polling , for the first time, that shows Trump's support dropping dramatically among Republican voters.

The ability of reporters to continue their work will shape public understanding of the ongoing drama. And the effectiveness of sympathetic conservative journalists in spinning alternative narratives should be interesting to watch.

Leaks have been steady, as was evident on Friday, and they will likely come at a faster pace. In the face of this pressure, and with President Trump potentially distancing himself from members of his team, some figures in the White House may well start to openly break with the administration in order to protect themselves. Should they speak, either to Mueller or to the public through Congress, this could change the game.

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Scandals are unpredictable

Then there is always the influence of crisis both at home and abroad. Events have a way of overtaking national discussions. It is possible that some major crisis, from a terrorist attack to turbulent stock markets, will so affect the national psyche that the Russia scandal loses its hold on the public conversation.

That's not inevitable, of course. In the middle of the Watergate scandal, there was a major war in the Middle East and the US subsequently suffered through a major oil shortage. Yet the Watergate investigation only got stronger.

Even though they are in the minority, the judgment of congressional Democrats will also be tested. During the battles over President Bill Clinton's impeachment, the attitude and approach of Republicans turned public opinion against them. The public came to see the Republicans, rather than the President, as the problem.

In the minds of many Americans, Republicans were ruthlessly partisan and intent on bringing down Clinton by any means. Clinton's approval ratings soared as he turned the narrative away from his wrongdoings and toward the idea that the entire process was purely biased.

Democrats will need to find a balance in the coming months by continuing to press for a thorough investigation without allowing President Trump to make them seem like partisan zealots who are manufacturing accusations to compensate for Hillary Clinton's loss.

It is a big mistake to assume scandals will unfold in any particular way. History shows that they can blow up, they can fizzle or they can simply linger.

As is usually the case, politics will be the key factor in determining whether this scandal, like the Iran-Contra affair of the 1980s, fizzles or whether, like Watergate, it brings down a president and transforms a nation.