WASHINGTON -- Donald Trump woke up Wednesday morning basking in the opprobrium of the entire Washington political establishment.

The reality-TV-star-turned-presidential contender was not just the unspoken target of Barack Obama's state of the union address.

He was also the unnamed antagonist in his own party's reply to the speech, delivered by South Carolina Gov. Nikki Haley.

Both speeches warned against immigrant- and minority-bashing in a country that owes much of its historic prosperity to the labour of immigrants.

From hundreds of kilometres away, Trump once again managed to wiggle his way into the centre of Washington's political conversation.

And he scoffed in the general direction of its disdain.

"The state of the union speech was one of the most boring, rambling and non-substantive I have heard in a long time. New leadership fast!" he tweeted.

Trump called Haley weak on illegal immigration in a "Today Show" interview. He also mused that she was off to a bad start if she wanted to be his pick for vice-president.

Trump has horrified the political establishment with his call for the mass-deportation of undocumented Latino migrants and a freeze on Muslim travel to the U.S.

The reaction to Tuesday's speeches showed that the starkest divisions in U.S. politics aren't merely between the parties -- but within them, as Republican elites align against much of their party rank-and-file.

Haley reminded viewers that she was the daughter of immigrants from India.

And she, the Republican party's chosen spokesperson for the biggest evening on the U.S. political calendar, delivered a staunchly pro-immigrant message that declared no foreigner willing to work hard should feel unwelcome in the U.S.

"During anxious times, it can be tempting to follow the siren call of the angriest voices. We must resist that temptation," she said.

Haley confirmed Wednesday that Trump was one of the people she had in mind when she uttered those words.

As for Obama, he delivered a riff on Trump's campaign slogan -- "Make America Great Again."

In his final speech to Congress, the president said that the genius of the country was its perennial willingness to embrace change -- and ability to ignore the angriest anti-foreign voices "promising to restore past glory."

Obama then specifically mentioned Muslims.

"We need to reject any politics that targets people because of race or religion," he said.

"When politicians insult Muslims, when a mosque is vandalized, or a kid bullied, that doesn't make us safer. That's not telling it like it is. It's just wrong."

Democrats in the chamber cheered loudly. Behind Obama, the Republican congressional leader Paul Ryan gently nodded to signal his agreement.

These are sensitive topics within the Republican party.

Indeed, some prominent conservative voices later expressed disbelief that the party establishment appeared to have opposed Trump -- instead of embracing his populist message.

Radio host Laura Ingraham said the party should be sympathetic to his message on illegal immigration -- and side with American workers struggling to compete with cheap foreign labour.

Conservative commentator Ann Coulter put it more crudely: "Trump should deport Nikki Haley."

And that prompted the chairman of the South Carolina Republican party to defend the governor, and to call Coulter's remarks "despicable."

The divisions in the party pitting its business wing against the anti-establishment ranks will be a prominent theme in the upcoming nomination races -- which start next month in Iowa, New Hampshire, and South Carolina.

The winner of those contests goes on to the general election, which will decide who delivers the next state of the union.