Al Franken, his wife and his daughter all tell PEOPLE that the Minnesota senator will not challenge President Trump in 2020

Sen. Al Franken Is 'Flattered' by Buzz, But Definitely Not Running for President in 2020

Al Franken, his wife and his daughter are unanimous—and firm: The senator from Minnesota and Saturday Night Live alum will not be running for president in 2020.

“Yeah, I’m not going to do that,” says Franken.

Get push notifications with news, features and more.

“It’s not going to happen,” adds his daughter, Thomasin, 36.

The senator’s wife, Franni, puts it most simply: “No.”

In at-home interviews for this week’s issue of PEOPLE (on newsstands Friday), the Franken family was unusually definitive in shutting down this spring’s buzz about Al, 66 and a former writer and performer on Saturday Night Live, being a contender for the 2020 Democratic presidential nomination.

“It’s very flattering, really,” says Franni, 65. “It’s kind of an affirmation that Al did exactly what he said he would do, be a work horse and not a show horse.”

For Thomasin, 36, a manager for Washington, D.C., public schools who lives with her husband and two young children two blocks away from her parents, there’s no sense playing the verbal dodge ball that is typical of might-be candidates who coyly keep their options open.

“There’s nothing to hedge,” she tells PEOPLE. “I think I understand how people are feeling. I was just at a party with people I hadn’t seen in a long time and they were all asking if he was going to run and they were hoping he would. No, thanks.”

Franken’s name made it onto the pundits’ list of potential 2020 candidates back in January, when he became a viral-video hit for his sharp questioning of President Trump’s controversial pick for Education Secretary, Betsy DeVos. It was an early act of the so-called Resistance by Franken, the former comedy writer who asserts in his new memoir Al Franken, Giant of the Senate that Trump’s presidency so far amounts to “constant, constant, constant lying.”

Image zoom Peter Zambouros

Franken, who is up for reelection in Minnesota in 2020, tells People he’s focused now on fixing President Obama’s Affordable Care Act, fighting the “just dreadful” House Republican health-care bill, and making sure that the special counsel investigating the Trump team’s ties with Russia has what he needs to get to the bottom of what Franken calls “pretty alarming stuff.”

WATCH THIS: People at the White House: The Final Interview with The Obamas