In contrast to the first presidential debate, where moderator Jim Lehrer was criticized for allowing Mitt Romney and President Obama to speak over him, vice presidential debate moderator Martha Raddatz won praise for pushing Paul Ryan and Vice President Biden for more specific answers.

The Washington Post’s Dan Zak described the scene on stage Thursday night:

A pro debated a novice Thursday night on national television, and both men were schooled by the moderator across the table.

Both candidates are auditioning for the vice presidency. Based on their performances — not their policies — only Vice President Biden acted as though he could sit at the desk in the Oval Office and have his feet touch the ground. Moderator Martha Raddatz, a journalist who’s more accustomed to flying in a Black Hawk than sitting at an anchor’s desk, pursued each man with the vigor of a woman more accustomed to needling foreign leaders than reciting prompter text.

Raddatz held firm control of the debate without squelching dialogue or spontaneity. She pushed the men for “specific plans”; she declared, “We’re gonna move on” when answers meandered; and she silenced both debaters with the teacherly interjection of “Gentlemen.” Fairly or not, she reserved most of her skepticism for Ryan.

“No specifics, then?” she asked Ryan about his ticket’s tax plan. “Can you guarantee this math will add up?... How do you do that?... I wanna know how you do the math.”

The AP reports that Raddatz’ performance was criticized by some Republicans:

Twitter was alight with praise for Raddatz, including some suggestions that she run for vice president.

“Martha Raddatz is no joke,” tweeted CNN anchor Don Lemon. “Following up and in charge.”

But some Republicans suggested Raddatz was being too quick to cut off Ryan and allow Biden to interrupt the Republican.

“Martha Raddatz is the worst moderator ever,” Fox News Channel host Sean Hannity tweeted. “Maybe next time Paul Ryan should invite her to his wedding.”

That was a reference to a story that circulated in conservative media earlier this week noting that when Raddatz married a Harvard law school student in 1991, one of the wedding guests was her new husband’s fellow Harvard student and future president Barack Obama. Raddatz and her husband, Julius Genachowski, divorced six years later.

Her final question was whether either of the two candidates had ever been embarrassed by the tone of the campaign. That drew a rebuke from Karl Rove, whose American Crossroads super PAC helps fund anti-Obama advertising. Rove tweeted that Raddatz’s question was “her own personal editorial.”

 The Washington Post’s She the People blogger Suzi Parker writes that Raddatz’s style of questioning was a welcome reprieve from political interrogation, perhaps due to her history as a national security and foreign reporter:

When Raddatz opened abruptly with a question about Libya, you knew she was going to play hardball better than Chris Matthews and knew her topic as if she were briefed by Hillary Clinton.

That’s because Raddatz knew her subject matter.

Her bio on ABC’s Web site is filled with accomplishments and adventures. “In 2011 she reported exclusive details on the raid that killed Osama bin Laden. That same year she had an exclusive interview on the USS Kearsage off the coast of Libya with the Marines who helped rescue two American pilots who had gone down in Libya. In 2012, Raddatz was on a USS destroyer as it made its way through the Strait of Hormuz.”

Raddatz, who joined ABC in 1999 as its State Department correspondent, has traveled the globe, covering wars, conflicts and terrorism. The author of a 2007 book “The Long Road Home: A Story of War and Family,” she’s a modern day Martha Gellhorn, the kind of journalist that little girls read about in history books and dream of becoming.

Overall, the Fix’s Chris Cillizza named Raddatz as one of the night’s winners.

* Martha Raddatz: Moderating a rhetorical fistfight is no easy task.  Raddatz did well to try to give both candidates equal time, keep them on the question asked and insert her own expertise — particularly on foreign policy — when it was necessary and appropriate.  A job well done under remarkably adverse circumstances.