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Some Republicans, most of them from the establishment, are concerned that if King runs for the Senate he could hurt the GOP's chances of winning an open seat because of past controversial statements and positions. Longtime Sen. Tom HarkinTom HarkinDistance education: Tumultuous today and yesterday Grassley challenger no stranger to defying odds Clinton ally stands between Sanders and chairmanship dream MORE (D-Iowa) is retiring at the end of his term, and Rep. Bruce BraleyBruce BraleyTen years later, House Dems reunite and look forward Trump: Ernst wanted 'more seasoning' before entertaining VP offer Criminal sentencing bill tests McConnell-Grassley relationship MORE (D-Iowa) is the likely Democratic nominee.

King pushed back in the appearance against the GOP's recent rebranding efforts, arguing Republicans should continue to embrace the "full-spectrum of our conservatism" rather than soften their stances on issues like gay marriage or immigration.