Just hours after Donald Trump was named the 45th president of the United States, Trump’s campaign manager Kellyanne Conway gave an interview with “CBS This Morning” discussing how Trump’s Democratic foes reacted to the stunning upset.

Of Trump’s conversation with opponent Hillary Clinton -- which came shortly after the Trump campaign made its way from Trump Tower to New York’s Hilton hotel -- Conway called it “brief” but “gracious.”

“My phone rang. And I handed it to Mr. Trump and he and Secretary Clinton had a brief but very gracious, very warm conversation,” Conway said. “He commended her on how smart and tough she is and what a great campaign she ran, and she congratulated him on his victory.”

Conway also divulged details of Trump’s conversation with President Obama, which she said lasted into the “wee hours” of the morning.

When Mr. Obama first called, Conway said, the president had reached out while Trump was still on stage giving his victory speech at the Hilton hotel in New York, “so the call was missed at first.”

“Timing is everything,” Conway said. “And of course [Trump] called him immediately when he knew that…that was also a very cordial conversation among -- you know, between two men who had been at battle, frankly.”

Conway added that Trump is “very excited for that meeting.”

“Mr. Trump looks forward to going down to the White House and meeting with President Obama and having a smooth transition,” she said. “You know, we can learn an awful lot from people who don’t support us.”

Of that possible White House meeting -- for which the president extended an invitation as early as Thursday -- Conway said the details were still being worked out.

Conway also weighed in on the campaign’s final two and a half weeks, saying their operation really came together around then to pull out a stunning victory.

“We had really navigated and survived a number of darker days here on the campaign,” Conway laughed. But, “we started to notice a few things - that we were becoming more competitive in some of these more traditionally blue states. And these are states like Michigan, Wisconsin, Pennsylvania, that are very attracted to the Donald Trump message.”

“The perfect storm was completed by Obamacare premiums increasing in October,” Conway said. “It really all came together.”