Washington(CNN) White House counselor Kellyanne Conway said Sunday that it was inappropriate and a "double standard" to be asked about her husband's tweets, which have been critical of her boss, President Donald Trump.

Since last year, George Conway, a prominent attorney whom Trump considered nominating for solicitor general, has been posting and retweeting tweets that have been critical of the President.

Asked about her husband's social media activities, Kellyanne Conway told CNN's Dana Bash on "State of the Union," "We're now going to talk about other people's spouses and significant others just because they either work at the White House or CNN? Are we going to do that? You just went there."

"By definition, spouses have a difference of opinion when one is, I don't know, draining the joint bank account to support things maybe the other disagrees with," she said. "This is a fascinating, cross-the-Rubicon moment and I will leave it at that."

Conway added that Bash's prompt "was meant to harass and embarrass" and suggested that she wouldn't have been asked that question if she were a man.

"I would ask you that if you were a man and your wife ... a thousand percent I would," Bash responded. "It's not about that. It's about questioning -- publicly questioning what you are doing for a living and with regard to your boss."

"There are other family members of people who work at the White House who certainly don't support the President privately and publicly," Conway said.

She continued: "There has been a different standard for me than there have been for other people. We bite our tongue plenty because I work for the people of this country, the United States government, and the presidency and the President of the United States, so there is plenty that I don't say."

Last Monday on ABC's "Good Morning America," Conway used fired FBI Director James Comey's disclosure that his wife and daughters supported Hillary Clinton in the 2016 election as a way to target his own political leanings.

"His people in his household wanted the other person to win," Conway said, referring to Clinton.

Shortly after Conway's interview on CNN aired, her husband retweeted a message from Maggie Haberman, the New York Times' chief White House correspondent, who has been a recent subject of the President's ire online.

Haberman tweeted a photograph of some of the living presidents and their spouses gathered at first lady Barbara Bush's funeral on Saturday. Other than President Jimmy Carter and first lady Rosalynn Carter, who were absent because of President Carter's overseas travel and Rosalynn's recovery from surgery, the only person missing was Trump.

Haberman tweeted the image with the comment: "When you contrast this photo with a weekend-long tweetstorm from current @potus, it's striking."