"The call was disgusting. It's reprehensible and it was appropriately denounced by the campaign," Sean Spicer, the RNC's chief strategist and communications director, told CNN's Erin Burnett on "Erin Burnett OutFront."
"But for him to then turn it back on them is almost as reprehensible. We live in a country of over 300-plus million people. Not everybody who supports Donald Trump, not everyone who supports Hilary Clinton, are exactly the kind of people that you want as supporters."
The Trump campaign distanced itself far more quickly than it has some other white nationalists in the past, including when Trump repeatedly demurred to CNN's Jake Tapper about David Duke's support, before finally condemning him.
But McMullin told CNN's Jake Tapper earlier Tuesday that he blamed the Trump campaign for the call that alleged -- without evidence -- that McMullin is gay because he is single.
"This is exactly the narrative, the approach of the Donald Trump campaign has had," McMullin told CNN about the call on Tuesday. "So it didn't even surprise when I heard news of the robocall, I just thought of course this is more of the same."
The call originated from a California man named William Johnson.
McMullin, who is originally from Utah, is polling close to Trump and Hillary Clinton in the typically reliably red state. Despite the polling, Spicer said Trump's campaign "will win Utah hands down."
He also sent a warning shot to Ohio Gov. John Kasich, who broke a pledge he made during his own presidential run to support the eventual nominee. Kasich wrote in 2008 nominee John McCain on his ballot rather than Donald Trump.
Spicer called it a "shame," adding the move will not bode well for Kasich.
"We'd love to have his support, think it would send a good message," Spicer said. "We're going to win Ohio regardless. And it's a shame because I think we could have won it more, or greater and bigger with John Kasich's support. But I think we are going to look back on this and it is not going to look good for the Kasich legacy."
John Weaver, Kasich's chief strategist, responded to Spicer after the interview, tweeting: "Spicer can't carry McCain's or Kasich's socks, but will keep his nose in Trump's jock, for another week. Legacies? Kenosha's? #Dontgothere"