Trump and Carson tied in Iowa, poll shows

Presidential candidates Donald TrumpDonald John TrumpGraham: America must 'accept the pain that comes in standing up to China' Weld 'thrilled' more Republicans are challenging Trump New data challenges Trump's economic narrative MORE and Ben CarsonBenjamin (Ben) Solomon CarsonCarson's affordable housing idea drawing undue flak Overnight Energy: Trump EPA looks to change air pollution permit process | GOP senators propose easing Obama water rule | Green group sues EPA over lead dust rules Green group sues EPA over lead dust rules it says are too lax MORE are tied atop the GOP field in Iowa, according to a new CBS News poll released on Sunday’s "Face the Nation."

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Trump and Carson are at 27 percent in the CBS News 2016 "Battleground Tracker," followed by Sen. Ted Cruz (R-Texas), who's in third place with 12 percent.

Two recent polls had found Carson in the top spot among Republicans in Iowa.

The poll also found that not only is former Florida Gov. Jeb Bush trailing at 6 percent, more than half of Republicans said they would be dissatisfied if he were the party's nominee. Though Trump is ahead of his competitors, the CBS poll found the majority of those supporting other candidates in Iowa would not be satisfied if he wins the GOP nomination.

Meanwhile, Hillary Clinton has made strides in the Hawkeye State following the first Democratic debate, now holding a 3 point lead over Vermont Senator Bernie Sanders.

Clinton's supporters picked her experience as a main reason they are backing her for the nomination in the CBS poll.

The poll showed Sanders's supporters are backing him for his policies on income inequality.