Disputes became popular during the Barrett hearings, when Feinstein closed out the procedures with an embrace for Senate Judiciary Committee Chairman Lindsey Graham, R-S.C., and public gratitude to Graham for doing a good job.
Feinstein, 87, said in a statement that she would not go after the role in the next Congress.
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No senator was wearing a face mask at the time of the embrace.
Democrats had strongly rejected Barrett's confirmation to replace the late liberal icon Justice Ruth Bader Ginsburg.
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"This has been one of the best sets of hearings that I've participated in," Feinstein said towards the end of the conference.
Those statements put her directly in the aim of some powerful liberals who had been skeptical for some time whether she was right for the job.
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"It's time for Sen. Feinstein to step down from her leadership position on the Senate Judiciary Committee," said Brian Fallon, the executive director of Demand Justice, which rejects conservative nominees to the courts. "If she won't, her colleagues need to intervene."
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Feinstein also bothered some of her associate Democrats at Barrett's first confirmation hearing, in 2017 for an appeals court, when she said that Barrett's hostility to abortion must be rooted in her faith and questioned if it would influence her rulings on the bench, saying the "dogma lives loudly within you."
Republicans exploited the statement, saying it was insulting to Catholics.
The criticism helped Barrett advance in the ranks of Supreme Court hopefuls.
Graham also took on the opportunity of Feinstein's words at the end of Barrett's hearings, often quoting them on the campaign trail in his reelection bid this year and using the denunciation to deprecate Democrats.
"I hate the fact that saying something nice about me, about the way I conducted the hearings, has gotten to the point now that people will drive you out of office," Graham said.
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Although Feinstein did not say why she was resigning from her role, she said she would focus her attention on wildfires and drought issues and the effects of climate change, which are critical in her home state.
She intends to continue to serve on the Judiciary, Appropriations and intelligence panels, but said she will not ask for the role of top Democrat on any of those conferences.
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