Hanks also talks about that viral Golden Globes martini photo while talking to Ellen DeGeneres.
Streep and Hanks stopped by "The Ellen DeGeneres Show" Tuesday following Sunday's memorable Golden Globe Awards, where Oprah received the Cecil B. DeMille Lifetime Achievement Award and followed it up with a rousing speech about social progress, the often-difficult and ugly trail it takes to get there, and the hard work yet to do. When Ellen referred to Oprah as "our future president," Streep applauded and pointed to Hanks: "And our future vice president!"
Oprah had barely stepped down from the podium when the hashtag #Oprah2020 began trending on Twitter Sunday -- and Streep is here for it, telling Ellen, "Where do I send the check?"
All jokes aside, Streep said Oprah is just the kind of president this country needs.
"We really thirst for that," Streep said. "We really want that kind of elevated, aspirational, can-do, optimistic attachment to the principles of our country."
She described Oprah's speech as a "barn burner," and Hanks joked that while Oprah was speaking, the pool water at the nearby Hilton Hotel actually separated.
Ellen also asked Hanks about the viral photograph of the actor carrying a tray of martinis back to his star-studded table.
"I was told to go get martinis," he explained. "It was like I was one of those truckers on mountain roads with a load full of Nitroglycerin. I have never been more nervous carrying something through a crowded space."
"She's on antibiotics because she's getting over the flu, so she couldn't have one," Hanks said of Streep.
"He brought four of them, and he brought them under my nose," Streep said, motioning with her hands how Hanks was taunting her.
Ellen was surprised to learn that Streep and Hanks had not worked together prior to filming "The Post."
"I had the days marked on the calendar of when I would show up to work and be in a scene with her at the same time," Hanks gushed.
Streep echoed his sentiments. "I was really glad to work with you because you're so funny, and we're in a serious movie. I knew that that injection of wit and style and getting the joke -- every real story, even the hardest ones, have something funny -- and you brought that."
The Hollywood heavyweights also stepped into each other's most memorable roles to impersonate characters including Forest Gump and "Devil Wears Prada" villain Miranda Priestly. See how well they do in the hilarious video below.