Concern about the rise of Republican presidential front-runner Donald Trump is now spreading from the GOP establishment to the Democratic hierarchy and the campaign of Hillary Clinton.

There is increasing agreement among political leaders of both major parties and by the Washington-based punditocracy that Trump can no longer be dismissed as a boisterous former reality-show host or a bizarre sideshow.

He has been leading the opinion polls for the Republican nomination for many weeks, indicating that his support is strong and durable, and he widened his lead in the latest CBS News-New York Times survey released last week. Thirty-five percent of GOP voters say they support the billionaire businessman, up from 22 percent in October. His closest competitor is Sen. Ted Cruz of Texas, with 16 percent, up from 4 percent in October. Sen. Marco Rubio of Florida has 9 percent and the rest of the GOP candidates have less than 5 percent each.

The informal non-aggression pact between Trump and Cruz has ended. Up to now, they have mostly avoided criticizing each other, but that stopped last weekend when Trump said Cruz is "a little bit of a maniac" because he habitually attacks GOP leaders in the Senate. Trump said Cruz doesn't have the temperament to be president. This is the same criticism, by the way, that many critics direct at Trump himself. Although their rivalry was muted during the Republican presidential debate in Las Vegas this week, the two are likely to square off with increasing frequency if Cruz continues to do well in the polls and threaten Trump's top standing in Iowa, which will hold the first delegate selection contest in February. The latest Des Moines Register/Bloomberg Politics poll finds that Cruz has recently moved past Trump there. He now has the support of 31 percent of Iowa Republicans and Trump has 21 percent, with the remaining GOP candidates far behind. Trump must feel the need to tear Cruz down.

Despite Cruz's surge, Trump's popularity within the GOP and his national following have injected a deep sense of worry not only into veteran Republican leaders but also the Democratic establishment, which still doesn't know what to do about Trump or how to slow him down.

This anxiety is clear in Clinton's campaign for the Democratic presidential nomination, where she is the overwhelming front-runner. She has exhibited concern about Trump's extremely tough stand on fighting terrorism in the aftermath of the attack in San Bernardino, Calif., in which 14 people were killed December 2. Trump has endorsed a ban on entry of non-American Muslims into the United States and monitoring U.S. mosques for possible terrorist activity. Clinton said Trump's view on Muslims is "not only shameful and wrong, it's dangerous" because it could help Islamic extremists recruit new operatives and adherents.

Trump then issued one of his most strident denunciations of Clinton ever. He said her policies as secretary of state under President Barack Obama "killed hundreds of thousands of people with her stupidity." He added in an interview with Fox News: "You look at what she did with Libya, what she did with Syria. Look at Egypt, what happened with Egypt, a total mess. ... She was truly – if not the – one of the worst secretaries of state in the history of the country."

In the past, Clinton has been dismissive of Trump. She laughed during an appearance on ABC News on December 6 when the former reality TV host's name was mentioned. "I'm sorry, I can't help it," she said. The next day, Trump proposed his ban on Muslim immigrants, which changed Clinton's attitude. In her harshest condemnation of him to date, she told a town hall meeting in Waterloo, Iowa December 9 that Trump deals "in prejudice and paranoia." On December 10, Clinton told late-night comedian Seth Myers on NBC, "I no longer think he's funny," and said Trump's comments had "gone way over the line."

The New York Times reports that Clinton and her aides "have had to rethink how they handle Mr. Trump and what his candidacy, and the anger in the electorate that has fueled it, means for her chances in 2016." Former Gov. Ed Rendell of Pennsylvania, who recently spoke to Clinton about Trump, told the Times, "She's as amazed as everyone else" by Trump's popularity.