The White House announced on Tuesday that it will not cooperate with the House of Representatives’ impeachment inquiry of President Donald Trump, calling it unfair and unconstitutional. By refusing to allow administration officials to testify and, in effect, denying that Congress has any legitimate right to impeach the president, the White House has pushed the country further toward a constitutional crisis. But this escalation from Trump’s efforts to pressure foreign governments to find (or manufacture) compromising information about his political rivals may also cost him critical Republican support

Trump’s major appeal as a presidential candidate in 2016 was his promise to obliterate the status quo. Both the Reaganite conservatism peddled by the other Republican contenders and the neoliberalism of Democratic candidate Hillary Clinton were essentially status quo philosophies. As president, Trump hasn’t implemented any significant populist policies, and his most significant accomplishments — the 2017 tax cut, appointments of right-wing judges, and executive orders revoking business regulations — have been standard conservative fare. But the impeachment crisis has thrown into sharp focus the ways in which Trump has in fact fulfilled his pledge to overthrow the status quo.

Trump’s blowing up any semblance of bipartisan cooperation, his attempts to divide the population along racial and ethnic lines, his casting the media as “the enemy of the people,” and his withdrawal from international treaties on trade, climate, and nuclear containment — these have been merely extensions of directions in which conservative Republicans already were heading. Republicans’ acquiescence to Trump’s disregard for debts and deficits has revealed that their supposed concern for fiscal responsibility was hypocritical all along.

But Trump’s contempt for the norms that previously had governed presidential conduct, his disinclination to distinguish between fact and fiction, his slander of the national security agencies as “deep state” enemies, his willingness to abandon allies (lately including the Syrian Kurdish forces), and his belief that Article II of the Constitution means that “I have the right to do whatever I want as president” — all of these are major departures not only from the status quo, but from the conservatism that has defined the Republican Party for the past four decades. And that makes the impeachment crisis dangerous for Trump.

The latest Washington Post-Schar School poll — conducted before the White House announcement that it would not cooperate with the impeachment process — shows that a majority of Americans endorse the impeachment inquiry and nearly half of all adults also think the House should recommend that Trump be removed from office. More surprisingly, support for the impeachment inquiry has risen 21 points among Republicans since July.

Republicans are not a monolith, and the 62 million Americans who voted for Trump did so for a variety of reasons. Many hoped that he would completely blow up the status quo, believing that they had nothing to lose. But many others voted for Trump largely because he was not Hillary Clinton, or because they believed that he would govern along the lines of past Republican presidents. They did not necessarily vote for Trump out of any conviction that a Republican president should be able to ignore Congress, that he should be free to use the machinery of government against his political rivals, that he should be above the law, or that his efforts should be guided by outlandish conspiracy theories.

It turns out that even many Trump supporters would like to retain those norms and principles that were established by the country’s founders and that have contributed to the country’s civic health and stability. The Mueller report’s murky conclusions about candidate Trump’s derelictions may not have moved Republicans, but the revelations about president Trump’s shenanigans with Ukraine seem to be giving them an uneasy feeling that lines were crossed that ought not to have been crossed. And assertions that the White House is above congressional oversight may make them uneasier still.

Democrats in Congress may conduct impeachment proceedings in a way that will turn public opinion against them. They may also lack the ability to compel government officials to testify, short of invoking Congress’ inherent contempt power that has been little used in modern times. But if the White House continues to stonewall the process, it seems increasingly likely that at least a few vertebrate House Republicans — particularly those who still believe in Congress as an institution — will come around to siding with the inquiry, and maybe even to supporting impeachment.

The indelible lesson of the Watergate scandal was that “It’s not the crime, it’s the cover-up.” It’s one thing for Republicans to argue that there was no explicit quid pro quo in Trump’s telephone conversation with the Ukrainian president. It’s quite another for them to agree that the president should be free to engage in witness tampering, destruction of evidence, and obstruction of justice, or that the legislative branch should be powerless to exercise its constitutional authority against the executive branch. Indeed, the more partisan the Republican, the easier he or she will find it to imagine that a corrupt Democrat at some point will occupy the White House. Should that dark day come to pass, wouldn’t they then regret having given Trump free rein?

The White House, in refusing to cooperate with impeachment proceedings, has raised the stakes of its clash with Congress. By redefining the crisis as an existential debate over the limits of presidential power, Trump may be in danger of losing those Republicans who still think of themselves as constitutional conservatives.