In an an interview with Ms Conway, who frequently speaks on behalf of the administration, veteran journalist and presenter Wolf Blitzer played clips from a rival channel from the day before, in which her husband was seen criticising Mr Trump.
Ms Conway’s husband, George Conway, is a Republican lawyer who has become well known as a spiky critic of the president, even while his wife worked for him as a presidential candidate, and then when he entered the White House.
“It’s a sensitive question and it’s a political question. It’s a substantive question,” said Mr Blizter.
“I don’t want to talk about your marriage, I know there are issues there. Your husband, George Conway, is a lawyer. I don’t want to talk about your marriage, I know there are issues there. Your husband, George Conway, is a lawyer....”
At that point, Ms Conway interjected, saying: “What did you just say. No, no, no. Did you just say there are issues there? You don’t want to talk about my marriage, but…?”
Mr Blister repeated his claim he did not want to talk about her marriage, and played a clip from MSNBC of Mr Conway attacking the president.
After he did so, Ms Conway said she was embarrassed for CNN. “Where is the shame, where is the introspection,” she said. “And the relevance is, and, come on—wait for it—drum roll—and he’s married to me?”
The Conways are not the first high-profile Washington DC couple that agree to disagree about politics. James Carville, who served as Bill Clinton’s campaign manager in 1992, is married to Republican consultant Mary Matalin.
At the same time, Mr Conway’s criticism of Mr Trump is frequently scathing. The president has sometimes, though not always, responded to the jabs. In March he called him a “a total loser” and the “husband from hell”, after Mr Conway suggested the president did not have the mental acutely to serve.
In her interview on Thursday, Ms Conway said to Mr Blitzer: “You embarrassed yourself and I’m embarrassed for you.”
“I looked up to you when I was in college and law school, I would turn on CNN to see what Wolf Blitzer had to say about war, famine, disruption abroad,” she added.
“I really respected you for all those years as someone that would give you the news and now it’s what somebody’s husband says.”