Senators are expected to adopt an order stipulating that Majority Leader Harriette Chandler serve as Senate President on all matters relating to the Hefner investigation.
Democratic U.S. Sen. Elizabeth Warren weighed in Monday, telling reporters "the charges against the Senate president's husband are disgusting and the people who have leveled these charges have a right to be heard and to be respected and protected". The men also said Hefner bragged about the influence he had over Senate policy decisions because of his marriage to Rosenberg.
WBUR's Steve Brown joined All Things Considered from the State House to discuss.
The top Democrat of the Massachusetts Senate stepped aside Monday after his husband was accused of sexual misconduct by several men.
Several men told the Globe that Hefner sexually assaulted or harassed them, including three men who said Hefner grabbed their genitals.
Several men came forward accusing Hefner of sexual assault and misconduct.
"I would like to take a leave of absence as your president, effective immediately, for the duration of the investigation", Rosenberg said in a letter to colleagues.
Rosenberg has recused himself and won't be involved in the investigation.
"Democrat Senators have questions to answer about the Senate President's leadership - given that they have the ability to determine his future".
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Rosenberg will remain a senator during the investigation.
Sen. Michael Barrett, a Democrat whose district includes Chelmsford and Bedford, said in a statement Monday morning that the "upsetting allegations" warrant an independent investigator, but "none of us is legally or morally responsible for the actions of our spouse unless we're aware of it and don't try to stop it".
Republican Gov. Charlie Baker, through a spokeswoman, called Rosenberg's decision to step down "the right one". Barbara L'Italien (D-Andover).
Rosenberg said Friday that he was devastated by the allegations and that Hefner would soon begin in-patient treatment for alcoholism. "The MassGOP is committed to holding these Democrats accountable on behalf of voters, who deserve answers", said MassGOP spokesman Terry MacCormack.
In an updated statement Monday night, Rosenberg said he looks forward to a "thorough, fair, and independent investigation". Succession talk is not a topic lawmakers usually like to go public with - loyalty playing the role that it does in politics - but there's a time and a place for everything, and senators appeared to be struggling with that question.
The Senate was expected to vote later Monday on a plan to appoint an independent investigator whose focus likely would be on whether Rosenberg knew about Hefner's alleged behavior, or if Hefner had any clout when it came to matters before the chamber.
L'Italien told reporters before entering the closed-door caucus that he did not see how alleged victims could come forward during the investigation if Rosenberg was still presiding over the Senate.
The picture was reportedly sent in a text message earlier this year.