"Is this really how he's going to spend his time as president?" CNN host Chris Cuomo asked Conway.
"He has over 25 million followers on Facebook and Twitter and it's a great way for him to take his message directly to people, cut through the noise or the silence," Conway said. "Important things that he's saying and doing are getting zero coverage."
"That's not what he's tweeting about," Cuomo pointed out. "He says that 'Hamilton' is overrated."
"That's his opinion," Conway replied. "I'm going! I'm taking my 12-year-olds for their birthday."
"But I'm saying, why take it up?" Cuomo said. "Why take up SNL? No president does that. Why take it up? Why waste the time? Why distract?"
"But why do you care?" Conway said. "Who is to say that he can't do that?"
She suggested that Cuomo focus instead on Trump's "unprecedented" meetings as part of his transition.
"So he doesn't take any responsibility for his own tweets," Cuomo said, sounding incredulous. "It's on me for focusing on that?"
"I didn't say that!" Conway said. "I didn't say he wasn't responsible."
Trump took to Twitter to demand an apology from the cast of the Broadway musical "Hamilton" on Saturday after the cast addressed Pence's attendance on Friday night with a statement read by Brandon Victor Dixon.
Watch their exchange: