Correction: An earlier version of this article incorrectly described the Senate’s consideration for Obama’s nomination of Richard Cordray to lead the Consumer Financial Protection Bureau. Senate Republicans blocked action on the nomination; it did not fail in an up-or-down vote. Obama later placed Cordray in the job with a recess appointment. This version has been updated.

President Obama’s raw exchange with the governor of Arizona on an airport tarmac this week did more than overshadow his carefully stage-managed road trip to trumpet his State of the Union goals.

The discussion revealed a testy side of the president’s personality that is at odds with his public image as “no-drama Obama,” reviving criticism that he is unwilling to be second-guessed — or to even entertain another point of view.

Shortly after stepping off Air Force One on Wednesday in Phoenix, Obama challenged Gov. Jan Brewer (R) over characterizations she made of him in a recent book. His reaction, coming one day after he used his State of the Union address to call for a renewed spirit of political bipartisanship amid the nation’s economic woes, has exposed him to accusations that he is not interested in working with Republicans.

Brewer, whose “Scorpions for Breakfast” faults Obama for pandering to Hispanic voters in his immigration policy, said the president mentioned the book, unprompted, after she invited him to meet with her to discuss “Arizona’s comeback.”

“He was somewhat thin-skinned and a little tense to say the least,” Brewer told Phoenix radio station KFYI on Thursday. “I went there with good intentions . . . talking about Arizona and how I could give some assistance to him.”

White House press secretary Jay Carney scoffed at the notion that a deeper meaning was to be gleaned from the brief exchange, calling it “political theater.” And Obama told ABC News anchor Diane Sawyer in an interview that it was a “classic example of things getting blown out of proportion.”

Denying that he was “tense” during the encounter, as Brewer described, Obama said, laughing, that he is “usually accused of not being intense enough.”

“I think it’s always good publicity for a Republican if they’re in an argument with me. But this was really not a big deal,” he said.

According to Carney, the president told Brewer that her description in the book of a meeting they had in 2010 in the Oval Office “was not accurate.”

At the time, Brewer had told reporters that her meeting with Obama was “cordial,” but in the book she described him as “patronizing” and said he lectured her.

Over the past year, as his relations with congressional Republicans have soured, Obama has tried to cast the GOP as rigid ideologues whose allegiance to tea party conservatives has nearly caused financial catastrophe — first when House Speaker John A. Boehner (Ohio) “walked away” from Obama’s “grand bargain” offer during summer debt ceiling negotiations and again when Republicans grudgingly adopted the president’s proposed extension of a payroll tax cut at the 11th hour.

But Republicans have painted a different picture. During the debt-ceiling fight, House Majority Leader Eric Cantor (Va.) told reporters that the president snapped at him in a negotiating session, saying “Don’t call my bluff” and abruptly walking out.

Republicans have more recently cast Obama’s “We can’t wait” campaign of taking executive action without congressional approval as evidence that he has chosen to ignore lawmakers. They characterized his recess appointment of Richard Cordray to head a financial consumer watchdog agency as the act of an imperial president intent on imposing his will.

At the same time, White House officials have pushed back hard against two recent books — one about Obama’s economic advisers and the other about the president and first lady Michelle Obama’s relationship — that portray an insular administration.

On Thursday, Sen. John McCain (R-Ariz.), Obama’s 2008 presidential rival, suggested that Obama’s reaction to Brewer revealed a well-known “prickly personality.”

McCain mentioned an account by Louisiana Gov. Bobby Jindal (R) of a meeting with Obama when the president visited his state after the Gulf of Mexico oil spill in 2010. According to Jindal, Obama accosted him on a tarmac about a letter Jindal had sent the administration asking for food stamps for those who had lost jobs.

“President Obama had personalized this. And he was upset,” Jindal wrote. “There was not a word about the oil spill. He was concerned about looking bad because of the letter.”

Richard Wolffe, a political analyst and author, said Obama probably had grounds to object to what Brewer wrote. He added, however, that presidents tend to grow more short-tempered with criticism over time because they are “in a bubble . . . surrounded by people who agree with them.”

Weiner reported from Washington.