Donald Trump terrifies Democratic leaders almost as much as he scares establishment Republicans, because they’re starting to come to terms with the possibility he could be the next president of the United States.

One of the few things on which the high-falutin’ folks in both parties can readily agree on is that he’s so odious they won’t mention his name in polite company.

President Barack Obama devoted the heart of his final State of the Union address to attacking Trump and his ideas. And if anyone was still wondering how top Republican officials feel about Trump, South Carolina Gov. Nikki R. Haley removed any questions by targeting him in the GOP’s official rebuttal to Obama, too. She called the real-estate mogul one of the “angriest voices” in the national political debate. But neither Obama nor Haley ever uttered the words “Donald Trump.”

Republicans say publicly and privately that they’re worried that Trump will win their nomination and then get shellacked in the general election, robbing the party of necessary support in congressional races. The truth, I suspect, is they are also concerned about him winning the presidency, which would empower the tea party wing of the party and marginalize insiders.

It’s that latter scenario that suddenly has Democratic elites wringing their hands.

For a long time, they seemed content to watch Trump wreak havoc on the Republican primary field. Now, though, it’s clear they’re alarmed at the possibility he could win the presidency.

And why wouldn’t they be?

Trump’s more open to policies that appeal to Democratic voters than any of the other Republicans in the race. Though he tends not to emphasize them in the primary — for obvious reasons — he holds or has held un-Republican positions on the social safety net, taxes, campaign finance, gay rights and other issues.

That is, he would be more likely as president to find common ground with Democrats in Congress than any of the other Republican candidates, most of whom have gotten to where they are through careful attention to party orthodoxy.

While his un-Republican positions on these issues won’t win over Democratic activists who are repulsed by his rhetoric on immigration and his inarguably loutish behavior on the campaign trail, they could present a threat to the Democratic nominee holding less sticky Democrats in place. That is, he could fray the Democratic coalition in a general election.

The Cassandras in the Republican primary have been shouting into the wind that Trump isn’t really a conservative. This has also occurred to Democratic operatives.

“As offensive as Trump is, we underestimate his threat at our own peril,” veteran Democratic strategist Chris Kofinis said. “I’ve heard too often about candidates who can’t win, who do. The country is divided and angry, and as bad as his ideas are, Trump will try to exploit this by appealing to those desperate for change.”

On Tuesday night, Obama recalled the politicians of past eras “who told us to fear the future, who claimed we could slam the brakes on change, promising to restore past glory if we just got some group or idea that was threatening America under control.” Of course, he’s not afraid that the late George Wallace will influence American voters or win the presidency.

He was talking about Trump in that passage and in this one: “We need to reject any politics that targets people because of race or religion. This isn’t a matter of political correctness. It’s a matter of understanding what makes us strong.”

Vermont Sen. Bernard Sanders understands the potential cross-over appeal of Trump well enough that he’s been trying to recruit the Republican front-runner’s supporters to his own campaign. While Hillary Clinton says it would be “amazing” to run against Trump, she’s also making the argument that Sanders is ill-equipped to defeat him — despite polls showing that Sanders currently fares better against Trump than she does.

Vice President Joseph R. Biden Jr. said this week on NBC he thinks “it’s possible” Trump could win the presidency.

My gut tells me Trump has the lowest floor and highest ceiling of the major candidates for the Republican nomination — that is, he could win big in November or fall flat on his face. But it’s that former possibility that suddenly has Democrats almost as nervous as Republicans about the prospects of Trump carrying the GOP banner in the fall.