Based on Clinton’s precedent, those costs will be paid against Trump’s agenda—things he wants to do but won’t achieve because of the distorting effects of impeachment on his political options and room for maneuver.

They will be paid by his associates—people whose reputations and ambitions will be permanently dented because of their proximity to him.

And they will be paid by conservatives who follow him—who will discover their own principles have lost credibility and power in the public mind because of their connection to Trump.

Understanding the real costs paid by a president during an impeachment battle requires engaging in some what-if scenarios. But these scenarios do not require lots of conjecture or long, speculative leaps.

The frayed center we live with today—with the enormous incentives for politicians to occupy rhetorical and ideological extremes—is not a new phenomenon. As Clinton began his second term in 1997, he believed he was supremely well-positioned to revive and vindicate that center. In an interview with me for the Washington Post a few days before his inauguration, he said his goal was to “flush the poison from the atmosphere” of the capital and of public life more broadly. In his second inaugural address, he quoted Scripture and asked Americans to join him in being “a repairer of the breach.”

On policy matters, Clinton’s notion of the center involved pushing both major parties against old natural instincts. For Democrats, that meant going against the grain on spending and trade, among other issues. For Republicans, it meant if they would surrender their instinctual hostility to government in general, Clinton would work with them in practical ways to create a society in which a robust, technology-driven private sector would work with an efficient future-oriented government to create more opportunities for average Americans.

But his primary objective wasn’t narrowly about policy. Clinton believed it was time to end the ideological and cultural wars, heal old racial wounds, and drain public life of its malice and addiction to conspiracy theory. As a newly reelected president and a son of the South, Clinton believed he was uniquely suited to this project.

A year later, these high-minded ambitions collided with the scandal surrounding his relationship with Monica Lewinsky. Once the battle began, Clinton lost all leverage to push his own party—he needed every vote, including those of liberals who had scant interest in his centrist vision—and he had zero pathway to engage even with sympathetic Republicans, whose party leaders brooked no opposition to their plan to evict Clinton from power. The new political and cultural center Clinton tried to create in the 1990s died during impeachment and is still dead.

Clinton wasn’t the only one to pay the price. Vice President Al Gore's obvious resentment of Clinton’s indiscretions and scandal turned him, for a season, into something of a head case—unable to decide how much to embrace Clinton’s economic and policy successes or repudiate his personal behavior. Gore didn’t handle the challenge well, but there’s no question the lingering smoke of impeachment was a genuine obstacle for him in the 2000 campaign. Imagine how different modern history would be if Gore had won the presidency (rather than just the popular vote) that year.

In Hillary Clinton’s case, the costs of impeachment likewise lingered. Even before the year of scandal, she often faced questions about her motives. But for many people, the scandal and the aftermath—staying with her husband and running for Senate—hardened the caricature of her as coldly single-minded in pursuit of power. The scar tissue she accumulated in the 1990s was clearly the inspiration for the private email server that caused such heartache. Imagine how different modern history would be if she had won the presidency (and not just the popular vote) in 2016.

What does this history have to do with Trump?

He is used to bullying and insulting fellow Republicans to get his way. Like Clinton, he will suddenly find his ability to push his own party—either on political or policy questions—is deeply limited. Senate Majority Leader Mitch McConnell has already signaled to Trump that he needs to put a sock in it when it comes to criticizing GOP senators.