CHAPIN, S.C. — South Carolina Gov. Nikki Haley endorsed Sen. Marco Rubio’s presidential bid Wednesday evening, giving him an extra boost as the Republican establishment’s embrace of the onetime insurgent grows, and he emerges as the chief alternative to Donald Trump and Sen. Ted Cruz.

Ms. Haley’s endorsement may not swing many votes — her 2012 backing didn’t help Mitt Romney, who lost the state’s primary to Newt Gingrich — but it signals Mr. Rubio’s ascendance.

“I wanted somebody with fight. I wanted somebody with passion. I wanted somebody that had conviction to do the right thing, but I wanted somebody humble enough that remembers that you work for all the people,” she said at a rally in Chapin.

The governor made the announcement as the fight in South Carolina boiled over ahead of Saturday’s vote.

Mr. Trump has sent a cease-and-desist letter threatening to sue Mr. Cruz, demanding he pull down an ad highlighting Mr. Trump’s former pro-choice position. Mr. Cruz on Wednesday dared Mr. Trump to file, saying he would love the chance to get the billionaire businessman in court, where he would have to answer pointed questions about his record — “under oath.”

Mr. Cruz also released an ad eviscerating Mr. Rubio for writing the 2013 Senate bill to grant illegal immigrants citizenship rights, juxtaposing video of Mr. Rubio and Mr. Obama making the same arguments for its passage. The ad ends with an image of Mr. Rubio in the same red and blue hues of the famous 2008 Obama “HOPE” campaign poster.

Known for sharp-elbow campaigning, South Carolina is living up to that reputation this year, with Mr. Cruz throwing most of the jabs — and taking most of the incoming fire from the other candidates, who say he is lying about their records.

Mr. Trump also again accused Mr. Cruz of having stolen the Iowa caucuses this month when his campaign, extrapolating from a report on CNN, told voters that retired neurosurgeon Ben Carson was dropping out — potentially boosting Mr. Cruz’s vote total at the expense of Mr. Carson.

Mr. Trump said voters can’t let that happen again and shouldn’t reward Mr. Cruz for his behavior.

“Here’s a guy, he raises [his hand on] the Bible, and yet he tells fibs, he tells lies, and then he does this stuff to Carson, and he does other things,” Mr. Trump said at a rally in Walterboro. “Politicians are bad people, boy, they are bad.”

Mr. Trump predicted that if he can win the South Carolina primary, he may run the table on the rest of the contests.

He is leading in polling in South Carolina, but a shocking survey from NBC News and The Wall Street Journal found Mr. Cruz has overtaken Mr. Trump in national polling, 28 percent to 26 percent. Mr. Rubio trails at 17 percent, followed by Ohio Gov. John Kasich at 11 percent, retired neurosurgeon Ben Carson at 10 percent and former Florida Gov. Jeb Bush at a dismal 4 percent.

“There’s a new national front-runner on the Republican side,” Mr. Cruz crowed Wednesday afternoon.

Most other national polls, however, put Mr. Trump much higher. A Quinnipiac survey also released Wednesday showed Mr. Trump at nearly 40 percent nationally — more than Mr. Rubio and Mr. Cruz combined, at 19 percent and 18 percent respectively.

Mr. Kasich won support of South Carolina’s largest newspaper, The State, which said voters had a unique chance to break partisanship in Washington by picking the Ohio governor. A USA Today/Suffolk poll found that Mr. Kasich is the strongest Republican candidate in a general election, topping Democrat Hillary Clinton by a whopping 11 percentage points in a hypothetical November match-up.

Losing out on the endorsements of the newspaper and the governor, Ms. Haley, was a blow to Mr. Bush, whose claim to be the chief anti-Trump candidate is quickly fading. He has seen no apparent boost from having his brother, former President George W. Bush, join him on the campaign trail in the Charleston area Monday.

After spending weeks trying to kneecap Mr. Trump, Mr. Bush switched tactics Wednesday and aimed his fiercest barb at Mr. Rubio, saying the first-term senator’s record doesn’t stand up to his own as a two-term governor.

Mr. Rubio, meanwhile, stayed mostly positive as he collected Ms. Haley’s endorsement. She joins his other top supporters from the state, Sen. Tim Scott and Rep. Trey Gowdy, signaling that Republicans are coalescing around Mr. Rubio and hoping he emerges as the chief alternative to Mr. Trump.

Mr. Cruz honed his argument that he is the only consistent conservative in the race and said his opponents are trying to hide their own records by accusing him of lying.

“Ethics matter,” Mr. Cruz said at a press conference called to battle back. “Their strategy of screaming ‘liar’ whenever anyone points to their record, and relying on fabrications, is not indicative of candidates running honest campaigns.”

Rather than dismissing Mr. Trump’s cease-and-desist letter on the abortion ad, Mr. Cruz called his press conference to dare Mr. Trump to file a full lawsuit, saying that would mean they would have to go to court over the veracity of Mr. Cruz’s ad, replaying a 1999 interview in which Mr. Trump says he is pro-choice and would not ban partial-birth abortion.

Mr. Trump says he has evolved on the abortion issue and is now pro-life.

”Donald Trump does not want to be under oath answering questions about his own record,” Mr. Cruz said.

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