What the candidates at the Republican debate must do to make their mark

As Republican presidential candidates prepare to meet Tuesday night for their fourth debate, they will be striving to make a mark among a winnowed field on the main stage of the Fox Business Network’s debate.

The smaller crowd gives the seven men and one woman participating in the prime-time face-off greater air time to make their case — or more opportunities to stumble.

Here’s a look at the candidates and their key goals Tuesday night, less than three months before the first ballots are cast:

Carson and Rubio

With surging polls comes surging scrutiny. The crucial issue for Ben Carson, a mild-mannered retired neurosurgeon, and Marco Rubio, a senator from Florida, is whether they can credibly, confidently answer questions about their past under the hot stage lights. Will they stick to their tactic of blaming the media for turning minor misstatements or missteps into big deals?

Carson has climbed slightly past Donald Trump in several national and state polls. Rubio has gathered enough support in surveys to firmly plant himself among the second tier of candidates, outperforming fellow Floridian Jeb Bush, whose campaign has stumbled badly.

In recent days, Carson was accused by Politico of fabricating an offer of a full scholarship to West Point. CNN spoke to several people who knew Carson growing up and could not find any who confirmed Carson’s tales of struggling with a violent temper and trying to stab a friend.

The Wall Street Journal could find no evidence to support stories Carson has told about protecting white high school classmates from rioting black students, or being the sole student to pass an honesty test given by a Yale University professor.

Carson and his campaign have stood by the stories and accused the media of a “political hit job.”

Rubio has long faced questions about how he handled his finances, including rumors of lavish spending on a state GOP credit card, and mixing personal and political expenditures. Trump recently called Rubio “a disaster with his credit cards” who “certainly lives above his means.”

On Saturday, Rubio’s campaign released American Express statements that showed that Rubio charged $65,000 in party business in 2005 and 2006, significantly less than other state GOP leaders who held similar positions. The statements also showed that Rubio made eight personal charges totaling $7,200 that his campaign says he promptly repaid.

Bush

Former Florida Gov. Bush, the presumed front-runner when he entered the race, has much on the line. He has cratered in the polls, slashed staff costs, and is spending time reassuring worried donors and trying to reboot his campaign.

Bush has conceded that he is not the strongest debater among the field. On Tuesday, Bush must overcome his reticence and be more aggressive in getting equal time. He must look to deliver a memorable moment that would boost his campaign.

The most assertive appearance by Bush during a debate arguably led toone of his worst moments of the campaign. He tried to take on Rubio over his voting record in the Senate while running for president. Rubio deftly responded by pointing out Bush’s support of a GOP nominee whose voting record was far worse. Rubio then pointedly refrained from saying anything that would tarnish Bush’s accomplishments while accusing his former mentor of attacking him for political expediency.

Since then, Bush has widely acknowledged that he needs to improve and his campaign rolled out a new slogan: “Jeb Can Fix It.”

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“I’m going to get better. I ought to get better. I know I have to get better,” Bush told reporters a few days after the last debate.

Trump

After being an unpredictable force of nature during the first two GOP debates, Trump nearly faded in the background during the third face-off last month (as much as the reality television star can fade into the background anywhere).

He was more subdued, largely avoided attacking his rivals and erred when he said he never criticized Rubio for aligning himself with Facebook founder Mark Zuckerberg over more visas for immigrants with specific skills. A moderator pointed out that Trump’s website called Rubio “Mark Zuckerberg’s personal senator.”

The change in tone occurred after Trump trailed Carson in some polls.

In recent days, Trump has taken to brutally criticizing Carson’s and Rubio’s records. Will this version of Trump — the swaggering showman eager to cut down his rivals — show up again Tuesday?

Cruz

Texas Sen. Ted Cruz has risen into the second tier of candidates alongside Rubio. A renowned debater at Princeton University, Cruz had a high point during last month’s GOP debate, when he excoriated the moderators for showing bias against conservatives. The crowd roared with approval.

Cruz is despised by the GOP establishment and many of his fellow senators, which fuels his appeal to voters who are tired of status-quo politicians. A breakthrough moment Tuesday night could help build his appeal among those voters, many of whom are backing Trump or Carson.

The rest

Fox Business Network dropped New Jersey Gov. Chris Christie and former Ark. Gov. Mike Huckabee off the main stage for barely registering in the polls. Kentucky Sen. Rand Paul, Ohio Gov. John Kasich and former Hewlett-Packard Chief Executive Carly Fiorina were fractions of a point away from the same fate. They need to catch voters’ attention to retain their place in the next GOP debate, in Las Vegas in December.

seema.mehta@latimes.com

Twitter: @LATseema

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