Last Tuesday was not a good day for President Trump. Within minutes his former lawyer, Michael Cohen, pleaded guilty to charges including a campaign finance violation, and his former campaign manager, Paul Manafort, was found guilty on eight counts, including fraud charges. So, not a banner day for his presidency. But was it a day that fundamentally changed it?

I don’t mean to ask whether it changed the trajectory of his presidency. On that, time will tell, etc. etc. Instead, I’m interested in something more core to Trump’s presidency as it currently exists. Has the guilt of Trump’s aides affected his ability to govern?

Max Boot, a writer for the Washington Post, addressed this question in a recent article: “Trump is now an illegitimate president whose election is tainted by fraud,” he wrote. Illegitimate. That word caught my eye, in part because presidents rely upon legitimacy to enact their agenda. Without it, their power can quickly erode.

“Legitimacy” can sound like a vague concept, but it has some clear definitions as far the presidency is concerned. Political scientist Ian Hurd defined it as “the belief that a rule, institution, or leader has the right to govern.” So will last Tuesday’s news undercut Trump’s democratic authority? Change everything? Reveal new vulnerabilities in the administration’s right to hold power? Not so fast. Legitimacy is complicated and takes many forms.

Electoral legitimacy

Trump’s electoral legitimacy was a complicated issue long before Cohen and Manafort’s legal troubles. Trump lost the popular vote to Hillary Clinton. Then there’s the Russia investigation — special counsel Robert Mueller may yet find something that invalidates the entire 2016 election result. (Some might argue that he already has.) All those factors should, at least in theory, make electoral legitimacy a weak spot for Trump — vulnerable to new information about campaign finance practices or possible ties to foreign governments.

But research doesn’t necessarily point us to this conclusion. That’s in part because elections are cultural events as much as political ones, and narratives of the 2016 election are well-established. The 2016 result has been interpreted by the media to mean that Americans wanted change, and that they were dissatisfied with the status quo. We’ve covered the racism and sexism angles, and there have been plenty of profiles of Trump voters. A challenge to Trump’s electoral legitimacy will have a difficult time undoing all that.

Indeed, my own research on how presidents interpret elections suggests that as election margins have grown narrower and politics have become more fiercely partisan, presidents have worked harder to create narratives of electoral legitimacy. These narratives increasingly rely on ideas about the relationship between presidents and the voters who elected them – rather than the entire country. Trump has certainly continued this, and it’s not clear that recent revelations will hurt him with his partisan base.

So, in practice, Trump’s electoral legitimacy doesn’t really rest on the magnitude of his win but rather on the narrative built around it. And that narrative is pretty strong.

Legal legitimacy

The mounting legal issues among Trump associates, on the other hand, could spell more trouble. If Cohen’s claims about the president and campaign finance are further clarified and supported, then it’s possible that a clear violation of law would hurt Trump’s legitimacy. If a few more prominent Republicans – particularly ones who are staying in Congress – spoke out against him, that might start to change the tenor of his presidency.

That said, it’s not guaranteed that even clearcut legal violations will seriously undermine a presidency. Back in 1998, polls found that Americans thought Bill Clinton had lied, and even obstructed justice, but that wasn’t enough to get them to support removing him from office. There appears to be some room for presidents to break the law, as long as people are happy with the direction of the country in general, or perceive the other side as worse. Trump has also tried to downplay the importance of campaign finance laws. It’s not clear that this strategy will work. But many Americans think that money in politics is already a problem, so violating the laws in place might not damage legitimacy that much beyond existing levels of disgust with the system.

Trump, of course, isn’t Bill Clinton. He’s more unpopular, and that could make a big difference. In August, 1998 (about a month before the House Judiciary Committee began considering impeachment articles), Clinton had net approval rating of about +30 percentage points, according to FiveThirtyEight’s approval tracker. Right now, Trump has about a -12 point net rating. Clinton’s popularity helped reinforce his claim to the presidency even as it became clear he broke the law. It helped to keep Democratic officials from breaking ranks, for example. Trump doesn’t have that shield at the moment.

In fact, Trump has frustrated politicians in both parties with his illiberal comments, and fallen outside the bounds of democratic values at times. That Trump has ticked so many people off may make it easier for them to question his legitimacy now that he’s in some legal trouble.

What it all means

Looking at the different dimensions of legitimacy makes it seem less obvious that the recent guilty pleas and convictions of Trump associates will fatally undercut his administration’s ability to govern. Distrust in the political system is already high. The Clinton case showed that the American public has some tolerance for legal problems, and once a president is in power, questioning his right to be there really undermines the stability of the system. The Constitution doesn’t provide a do-over option where elections are concerned. That, plus the narrative weight of even a narrow win, makes the bar for questioning a president’s electoral legitimacy very high.

Instead, Trump’s most persistent source of legitimacy problems comes from the way he has governed, not how he got into office. At the same time, it’s not obvious that legitimacy can be separated from partisanship or attitudes toward policy, which doesn’t leave much hope for a shared set of standards or democratic values that cross party lines.

What about the long-term impact on the presidency, after Trump has left office and these particular scandals and policies are behind us? After Richard Nixon’s resignation, Congress adopted a number of new rules – including revamping the campaign finance regime, instituting “sunshine laws” and attempting to improve public access to government records. But it’s not totally clear that all of this improved legitimacy all that much. Congress might be in a good position post-Trump to make some reforms as far as things like releasing tax returns and divesting from business interests. But the real issue with legitimacy might have more to do with the president’s words and actions than with the election or even the law. Making more laws about transparency and campaign donations won’t protect the country from that problem coming up again.