Second, though presidents cannot impose their will on most of domestic policy, they can help define the issues on the political agenda. In the choices that he makes, Mr. Trump may play down conflict over the size and scope of government and shift the political debate toward questions of national identity, immigration and culture.

Finally, few Republicans are likely to want to cross Mr. Trump and his energized supporters given the threat of a potential primary challenge in 2018.

Consider, for instance, Mr. Trump’s decision to name as his chief strategist Steve Bannon, the head of Breitbart, a website described in an article in the conservative National Review as catering to “a small but vocal fringe of white supremacists, anti-Semites and internet trolls.” Though the move lacked recent precedent, no Republicans in Congress objected, which made the issue into a partisan dispute with Democrats. Mr. Trump has also stirred emotions by promising to deport two to three million undocumented immigrants. By contrast, the fate of a tax cut — normally the top G.O.P. domestic policy priority — has received less attention (though the party will almost certainly pursue one).

Mr. Trump’s success is likely to provoke a response from Democrats that could accelerate this shift. They face an outraged liberal base that is likely to reject conciliatory messages intended to win back votes among the white working class.

The party might instead double down on cosmopolitan appeals to the minority voters and college-educated white voters who were the main target of Hillary Clinton’s campaign. The strategy failed in 2016, but the incentive to try again is clear. Democrats came closer to winning several Sun Belt states where minority and college-educated white populations are growing, like Arizona and Georgia, than they did some traditional Midwest strongholds with higher numbers of noncollege whites, like Ohio and Iowa.

A focus on cosmopolitanism might make electoral sense for Democrats given the changing demographics of the country, but it could further weaken their appeal to whites without college degrees, dividing the electorate by race and class even more.

Nothing about this process is preordained, of course. Republicans may yet succeed in steering Mr. Trump toward a traditional G.O.P. agenda of tax cuts and deregulation. But the effects he could have on America’s party system could be of far more lasting consequence than almost any policy he might propose.