Top GOP presidential candidates Donald Trump, Ben Carson and Sen. Marco Rubio, R-Fla., all said Tuesday that they would oppose raising the federal minimum wage up from its current rate of $7.25 an hour, arguing that a higher rate would ultimately harm the poor more than help them.

In the Tuesday night Republican debate hosted by Fox Business and the Wall Street Journal, Ohio Gov. John Kasich countered them by saying a modest increase could help some people.

The candidates' opposition has come as Democrats have gotten bolder in pushing for a higher federal minimum. Front-running Democratic candidate Hillary Clinton has endorsed a $12 minimum, while her chief rival, Sen. Bernie Sanders, I-Vt., has called for a $15 per hour minimum wage.

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Asked during the GOP presidential debate if he was at all sympathetic to the protesters calling a $15 rate, Trump said he was not. "Taxes too high. Wages too high. We're not going to be be able to compete against the world. I hate to say it, but we're have to leave it where it is. People have to go out and work very hard to get to that upper stratum."

Carson, currently the front-runner in some polls, added that he would not raise it either, noting that he had worked minimum wage jobs as young man and that those jobs gave him valuable experience on how to "ascend the ladder of opportunity." He wouldn't have had that opportunity if the minimum wages were higher, he said.

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