GOP front-runner Donald TrumpDonald TrumpTrump showcases Cabinet picks on 'thank you tour' Trump: Time changed award to 'Person of the Year' to be 'politically correct' Feinstein after dinner with Clinton: She has 'accepted' her loss MORE has bumped Ted CruzTed CruzThe Hill's 12:30 Report Cruz defends Trump's Taiwan call Ark., Texas senators put cheese dip vs. queso to the test MORE from the lead in Iowa just a month before the first-in-the-nation caucuses, according to a new online poll.

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Trump, with 39 percent, has a 5-point lead among likely Republican caucus-goers over Cruz, a CBS News “Battleground Tracker” poll released Sunday morning shows. Marco RubioMarco Rubio House passes water bill with Flint aid, drought relief What the 2016 election can tell us about 2018 midterms Fight over water bill heats up in Senate MORE is in third place, with 13 percent.

Pollsters found that Trump cut into Cruz’s support among Tea Partiers and evangelicals in Iowa, CBS said.

The New Hampshire race is unchanged, according to the new poll, with Trump holding a wide lead over Cruz and Rubio. John Kasich is now in fourth place, however, replacing Gov. Chris Christie.

Trump also still holds a double-digit lead in South Carolina, CBS found.

The online polling firm YouGov conducted the poll for CBS. It has a 7.2 percent margin of error in Iowa, 6.8 percent margin of error in New Hampshire and 5.7 percent margin of error in South Carolina.