(Bloomberg) The Republican Party's leading presidential candidates clashed over how to reform the nation's financial system and handle immigration in their fourth debate on Tuesday, exposing deep rifts in the Republican Party and starkly different strategies for winning the election.

Republicans divided over changes to the U.S. tax code, with U.S. Senator Rand Paul of Kentucky saying he backed mortgage and charity breaks, while retired neurosurgeon Ben Carson disagreed. Carson, who backs a flat tax based on tithing, said Americans would give more to charities if they paid less taxes.

“People had homes before 1913 when we introduced a federal income tax,” Carson said. “We had churches before that and charitable organizations before that. The fact of the matter is, I believe if you put more money in people’s that they will actually be more generous, rather than less generous.”

U.S Senator Ted Cruz of Texas called for a flat tax where "every American pays 10 percent across-the-board," which he said would end loopholes that benefit the "Washington cartel." He added that his plan would abolish the IRS—along with the Departments of Commerce, Energy and Housing and Urban Development.

"There are more words in the IRS code than there are in the Bible, and not one of them is as good," the Texan said, to applause from a crowd.

One of the night's most fascinating exchanges came after U.S. Senator Marco Rubio of Florida described his tax plan, and said he was "proud" of its child tax credit. Paul then pounced, declaring Rubio's idea as counter to conservative principles.

"Is it fiscally conservative to have a trillion dollar expenditure? We're not talking about giving people back their tax money, he's talking about giving people money they didn't pay. It's a welfare transfer payment," Paul said, adding, "Add that to Marco's plan for a trillion dollar in new military spending and you get something that looks to me not very conservative.

"This is their money," Rubio countered. "They do pay it is refundable not just against the taxes they paid to the government, but also... on the payroll tax." The Rubio went for the jugular. "Yes I do want to rebuild the American military. I know that Rand is a committed isolationist, but I'm not."

Continuing his attack, Paul said of Rubio, "You cannot be a conservative if you're going to keep promoting new programs that you're not going to pay for."

Republican candidates turned sharply on the financial interests who have long underwritten the party. Former Florida Governor Jeb Bush, in a more animated performance than he has delivered in past debates, argued for higher capital requirements for banks to protect against another crisis, Ohio Governor John Kasich, a former managing director of the Lehman Brothers, blamed Wall Street for showing "too much greed," and Cruz said big banks "absolutely" never should be bailed out again.

Strikingly, Bush also didn't shy away from the issue of immigration, a topic that has gotten him into trouble with many conservatives. In so doing, he set off another one of the sharpest exchanges of the night by criticizing Donald Trump's plan to deport an estimated 11 million people now living illegally, arguing that it would weaken the party's chances for winning the White House.

"They're doing high-fives in the Clinton campaign right now when they hear this," he said. "We have to win the presidency, and the way you win the presidency is have practical plans."

The ensuing exchange illustrated the fault lines immigration has created in the party. Bush got support from Kasich, who called Trump's plan a "silly argument."

That triggered an immediate counter-punch from the co-front-runner Trump, who shot back that he's built an empire worth billions. "I don't have to hear from him," Trump said of Kasich. But Cruz, who noted that he is the son of immigrants, took the harder line more popular with the party's conservatives.

"If Republicans join Democrats as the party of amnesty, we will lose," he said.

Several of the candidates rejected a minimum wage hike, saying it will increase unemployment and put the United States at a competitive disadvantage.

"I hate to say it, but we have to leave it the way it is," Trump, a billionaire, said of the minimum wage, now $7.25 an hour as set by the federal government. "We can't do this if we are going to compete with the rest of the world."

Carson, who is running neck-and-neck with Trump in the polls, argued that raising the minimum wage leads to joblessness, "especially in the black community."

Though not all of the eight candidates on the stage addressed the minimum wage, Kasich was the only one who spoke up in favor of an increase.

After trying to reassure donors and supporters about his campaign's staying power following a poor debate performance two weeks ago, Bush entered Tuesday evening's Republican presidential face-off with more at stake than any of the other seven candidates joining him on stage at the Milwaukee Theater. The former Florida governor, who has seen his poll numbers collapse, pledged to be stronger this debate, and recovered in his first question after appearing initially nervous, winning applause when he called for a rollback of Obama's regulations and when he attacked both the president and his former secretary of state, the front-runner for the Democratic nomination.

"Hillary Clinton has said that Barack Obama’s policies get an A. Really? One in 10 people right now aren’t working or have given up altogether, as you said. That’s not an A," Bush said. "One in seven people are living in poverty. That’s not an A. One in five children are on food stamps. That is not an A. It may be the best that Hillary Clinton can do, but it’s not the best America can do." He was tart with Trump, telling his mocking nemesis at one point with elaborate sarcasm: "Thank you, Donald, for allowing me to speak at this debate."

In an earlier face-off for the four candidates who did not have the polling numbers to make it to the main event, both New Jersey Governor Chris Christie and former Senator Rick Santorum suggested that politics has motivated the Federal Reserve's policy of low interest rates. Santorum accused the Fed of "overprotecting" Obama.

Former Arkansas Governor Mike Huckabee defended his plan to shift from an income tax to a consumption tax, shrugging off concerns that it would put a damper on the economy. "Do you know an American who will just stop spending?" Huckabee asked. While Louisiana Governor Bobby Jindal attacked Christie as a "big government Republican," Christie focused his fire on Clinton, saying that "she will drown us in debt" and accusing former secretary of state of helping to engineer a "weak and feckless foreign policy" that has empowered China.

If he is elected president, Christie promised, "I'll fly Air Force One" over the islands Beijing is building in disputed waters of the South China Sea.

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