Meryl Streep and Hugh Grant's "imperfect" harmony in new movie

Meryl Streep and Hugh Grant are in "imperfect" harmony in their new movie, "Florence Foster Jenkins" -- imperfect, because it's based on a true story about a tone-deaf diva.

Streep plays Florence, a 1940s New York City socialite who dreams of becoming an opera singer, but lacks the musical talent. Unlike her on-screen role, Streep herself has proven to be a natural singer in "Mamma Mia" and "Ricki and the Flash" -- but not in this movie.

"I did have to learn nine very difficult arias because Florence Foster Jenkins picked the most difficult soprano coloratura in arias in the cannon," Streep told "CBS This Morning" Wednesday. "I did learn them, to sing them as well as I could, and then screwed around with them and try to make my accompanist laugh. That was my goal."

Florence Foster Jenkins did not let her lack of singing ability stop her. In fact, she went on to record and perform, and even sell out at Carnegie Hall, becoming famous for her lack of rhythm and pitch and an inspiration for her courage. She couldn't have done it without the encouragement of her husband, St. Clair Bayfield, played by Golden Globe-winning actor Hugh Grant.

Grant said he was nervous about acting with his iconic costar, a three-time Oscar winner who's earned 19 nominations.

"She tried to soothe me almost every day. I thought it'd make me feel better if I thought, 'well, Meryl's nervous as well,' so I used to say, 'Meryl, are you nervous?'" Grant said.

Streep admitted she was indeed nervous, especially "because I thought I was inflicting this sound on people."

Grant also had to do some training for his gig. While Meryl had to learn how to be a bad singer, Grant had to learn to dance well.

"It was a nightmare. You're reading the script thinking, 'I might be able to do that...' And you know, it's just something screenwriter dashes off, 'dances brilliantly.' You know, I'm stuck in a studio for three months, ladies in leotards," Grant said, laughing.

For both Streep and Grant, their latest movie is a diversion from their lives outside the big screen, where they are very much involved in politics. Meryl Streep -- who's been a vocal supporter of Hillary Clinton -- addressed the Democratic National Convention in Philadelphia last month. She said the experience was personal.

"It meant an enormous amount to me because I felt the press of history behind me," Streep said. "I felt my grandmother and mother imagining what they would feel. My mother was born before women could vote. It's very recent that we've been admitted to the United States with all of our rights, so I felt it. It was a moment in history and I felt like I was surfing this huge wage of wonderfulness."

Like his costar, Grant has also taken on a political role back at home in London. A victim of phone hacking himself, Grant is one of the most high-profile faces of "Hacked Off" -- an organization that speaks out against intrusive media coverage by the British tabloids. The group was founded in the wake of the News Corp. phone hacking scandal that revealed reporters spying on celebrities and royals. Grant said "Florence Foster Jenkins" was a good break from his work with the watchdog group, which has consumed much of his time in recent years.

"It was lovely because instead of you know, worrying about press regulation and change in the law and number of votes we can get in the House of the Lords, you're worrying about, 'what shade of makeup should I wear?' And it did feel relaxing," Grant said.

Grant also weighed in on the U.S. presidential election. While he said Britain is in "no position to laugh" -- alluding to the Brexit decision -- he called the campaign a "frightening comedy" where "quite scary people are coming to the fold."

While Grant said that he had no desire to be politically active in the U.S., Streep said her involvement was "tricky."

"I love being an actor. So it interferes with the thing I do -- dare I saw art, or the thing I love doing -- to be political, and so I try to stay out," Streep said. "But it keeps pulling me in because the other part of it, as a citizen right now, we are obliged to stand up and say, 'I don't -- this can't stand, this is impossible, this can't represent us.' So every person is obliged to do that. Even the most private people, like me."