▶ Watch Video: Kellyanne Conway says she’s advised Trump to wait until after midterms to announce 2024 bid

Former President Donald Trump is “chomping at the bit” to announce his third presidential bid, his former counselor and campaign manager Kellyanne Conway says. But she has advised him to wait.

“My advice to the president privately is my advice to him publicly, which is, ‘If you want to announce, wait until right after the midterms,'” she told CBS News’ Catherine Herridge in an interview Friday.   

Asked whether she thought Trump would announce he’s running, Conway retorted, “He would like to have done that already.” She said she spent time with the former president this week, and she told Herridge that should he run, “I’ll be a part of it.”

“This nomination is President Trump’s to have if he wants it, and very little will get in the way of that, but it’s a very personal choice for him,” Conway said.

That said, Conway understands that even if Trump runs, “there will be others who run — it will not be uncontested.” 

She has told him to watch for Rep. Liz Cheney, the vice chair of the House select committee investigating the Jan. 6, to announce her own run for the presidency, although “it’s not even clear she can win reelection in Wyoming.” Currently, Cheney appears to be trailing Trump-backed primary challenger Harriet Hageman — a recent poll showed her losing by 22 points.

Conway predicts that “dozens of people” will be running if Trump forgoes another presidential campaign and “very, very few people running” if he decides to enter the race. One of the most prominent possible challengers is Florida Gov. Ron DeSantis. Conway offers this advice to him: “I would say that ‘go be an unbelievable two-term governor, the best two-term governor of Florida in modern times, if not ever,’ and then he can run for president before he’s even 50.” 

She called former Vice President Mike Pence, whom she also spent time with this week, the “wild card.” 

“This is the guy who was right there with President Trump. It didn’t end on the best terms,” she said, adding that for four years they sang “from the same song sheet,” a “president and vice president who complemented each other’s styles but were of a single mind on the substance.”

While Pence still touts the Trump administration’s policies, in an understated way he says that the two “may differ on focus.” He implied this week that Trump’s ongoing focus on the 2020 election is misplaced. “Elections are about the future,” Pence noted at a conference in Washington.

Conway also contemplated the potential impact of the Jan. 6 hearings on Trump. Sure, there will be people who are “enraged” and will vote against him, she said, but the hearings may also make him “a little bit of a martyr.” As voters, she said, “we protest and pontificate in groups,” but we vote as individuals, “and we’re pretty self-interested when we do that.”

The truism she landed on in 2016 that she brought up again was that “voters vote according to what affects them, not just what offends them.” 

But as for Trump’s actions on Jan. 6, 2021, Conway says she’s “not sure what he was doing” for those 187 minutes when his supporters overran the Capitol, before he called on them to stop. 

Trump frequently communicated directly with his tens of millions of social media followers. “I do wish he had done that sooner,” Conway said. 

She recalled that on Jan. 6, 2021, she called the White House. Conway had left her job as counselor to the president a few months earlier to spend more time with her family.

“I placed a call to the White House asking him to certainly speak to the people and do more,” she said. “And I’m glad that he finally did that and told them to go home and to go in peace.”

Asked whether she succeeded in contacting him, Conway explained how it was she reached Trump that day. 

“I normally would call the president on one of his cellphones or usually through the switchboard, so it’s a secure call. I knew the switchboard would take – it would take too long because they’re doing their job,” Conway said. 

Instead, “I called the cellphone of someone I knew would be right next to the president. I didn’t even have that cellphone in my phone. I had to call my people who worked with me in my office” for the number, she said.  

“I made the call. This person said, ‘Would you like to talk to the president?’ I said, ‘No, I would not like to talk to the president. I would like him to tell people to get out of there, and I’ll call him later.’ I did speak with him,” Conway recalled, “later on or maybe early the next day.”

She said she knows her message was relayed to Trump, “and I wasn’t alone.” Others also prevailed on the president to act. “‘Add my name to the chorus of people who no doubt are running in there and burning up the phone lines saying, ‘please get people out of there.'” 

Exactly who talked to Trump during that period is still not entirely known. Internal White House records from Jan. 6, 2021 that were turned over to the House select committee show a gap in Trump’s phone logs of seven hours and 37 minutes, including the period when the Capitol was under assault, CBS News’ Robert Costa and Bob Woodward reported earlier this year.