(CNN) Democrats and allied liberal groups are on the defensive -- and cautiously weighing their next steps -- amid revelations of sexual harassment and assault by Minnesota Sen. Al Franken.

On Thursday morning, the broadcaster and former model Leeann Tweeden said in an account posted to the 790 KABC website that Franken had forcibly kissed and later groped her, while she was asleep, during a USO Tour overseas in 2006.

"I couldn't believe it. He groped me, without my consent, while I was asleep," Tweeden wrote . "I felt violated all over again. Embarrassed. Belittled. Humiliated."

The story included an image that shows Franken reaching for Tweeden's breasts as she slept, wearing a flak vest and Kevlar helmet.

"I certainly don't remember the rehearsal for the skit (in which Tweeden said Franken kissed her) in the same way, but I send my sincerest apologies to Leeann," Franken said on Thursday, before releasing a longer statement . "As to the photo, it was clearly intended to be funny but wasn't. I shouldn't have done it."

News of the report was jarring to progressive groups who count Franken, the former "Saturday Night Live" star and bestselling author, as one of their most popular draws and a potential presidential or vice presidential candidate in 2020. He was applauded by liberals during the Trump administration's confirmation hearings for taking a harder line than some of his colleagues with Attorney General Jeff Sessions and Secretary of Education Betsy DeVos. The revelations also diverted attention from the sexual abuse scandal facing Republicans: Senate candidate Roy Moore of Alabama is accused of making advances on teenagers when he was in his thirties.

The progressive group MoveOn.org on Thursday called the report about Franken "deeply disturbing."

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"Progressives & Democrats must not tolerate sexual harassment or assault," it said in a tweet . "We must lift up women & others speaking out. @SenFranken should be held to the same standard as anyone in public or private life."

But that standard -- how it's measured and then enforced -- could become a point of contention among Democrats.

"What accountability should look like is clearly an important question. As a next step, MoveOn strongly supports an immediate investigation by the Senate Ethics Committee," the group's chief communication officer, Nick Berning, said in an email.

Guy Cecil, chairman of Priorities USA, was critical of Franken's initial response to the charges.

"That was not an apology and was an insufficient response to serious allegations," he wrote . "Al Franken must be held accountable if our party wants to live up to our commitment to women & girls."

Top Democrats in Washington are expected to go along with Senate Majority Leader Mitch McConnell's call for an ethics investigation. None have called for Franken to resign.

"Sexual harassment is never acceptable and must not be tolerated," Minority Leader Chuck Schumer tweeted early in the afternoon. "I hope and expect that the Ethics Committee will fully investigate this troubling incident, as they should with any credible allegation of sexual harassment."

Neera Tanden, the president of the Center for American Progress, also expressed her support -- retweeting Missouri Sen. Claire McCaskill's own call -- for a probe into Franken.

"And I hope some women are part of the ethics investigation panel," she added in a subsequent post.

And I hope some women are part of the ethics investigation panel. https://t.co/E0BxXReopB — Neera Tanden🖖🏼 (@neeratanden) November 16, 2017

The abortion rights group NARAL issued a broad condemnation of sexual misconduct in "the traditionally male, very powerful Halls of Congress" and anywhere else, but mentioned Franken by name only to say it expects him "to be at the front of the line in addressing the impact of (elected leaders') behavior, and changing this destructive culture."

To Leeann Tweeden and all the women who have come forward with their stories of sexual harassment & assault: We support and believe you. Our statement: pic.twitter.com/RQv94JqYYB — NARAL (@NARAL) November 16, 2017

The Franken revelations are especially fraught for Democrats in the Trump era, as they seek to frame themselves in opposition to Republicans who support the President in spite of a series of unresolved allegations of sexual misconduct against him. More recently, Moore, the Alabama Republican, has been hit with a flurry of detailed accusations. (Top Republicans have called on Moore to stand down from his campaign.)

Other concerned Democrats, many clearly thrown for a loop by the Franken news, are beginning to think ahead to the coming midterms and future election cycles.

"We need elected officials without baggage, without regrets and without fake apologies," the progressive strategist Rebecca Katz said on Thursday. "The best way to make sure we get that is to nominate and elect young people who know better and women who wouldn't be put in these situations in the first place."

Rep. Ro Khanna, a California Democrat, called on Franken to "come completely clean about the details of what happened, and if there are any other incidents involving other women that may come to light."

Franken himself has been outspoken on the rising tide of sexual harassment and assault allegations now sweeping across American life, from Hollywood to the corridors of Congress. His past statements -- dating to his first run for Senate in 2008, when Republicans hammered him over a column he had written for Playboy magazine nearly a decade earlier -- will now be subject to sharper scrutiny and charges of hypocrisy.

On October 10, Franken shared an opinion piece , written by former Fox News host Gretchen Carlson, that detailed ways to assure "more victims have opportunities to speak up, and to see justice served when they do."

Franken introduced the piece on Facebook by writing: "The women who have shared their stories about Harvey Weinstein over the last few days are incredibly brave. It takes a lot of courage to come forward, and we owe them our thanks. And as we hear more and more about Mr. Weinstein, it's important to remember that while his behavior was appalling, it's far too common."

Ten days later, he tweeted: "I believe we should do everything in our power to support survivors of sexual violence."