Carson wins 28 percent in Bloomberg poll to Trump's 19 percent.
Clinton has an 11-point lead in new Quinnipiac survey of Iowa.
Donald Trump has a slight lead among GOP voters in the Sunshine State.
Poll is a welcome sign for Trump, whose rivals are catching up in other early-voting states.
Trump leads Carson by only 1 point in a Fox News national poll.
A new PPP survey shows Clinton with 42 percent support nationally.
The rising poll numbers come after a strong performance in Wednesday's debate.
Retired neurosurgeon Ben Carson follows Trump in second place in the Grand Canyon State.
Trump's net favorables are up 16 percentage points in the last two weeks; Bush is down 6.
Another poll found Sanders pulling within 7 points of Clinton.