Analysis by Stephen Collinson, CNN

(CNN) -- Republicans and the White House are mounting a robust effort to shield Supreme Court pick Brett Kavanaugh after an anonymous woman accused him of sexual misconduct in the 1980s, rocking his confirmation process.

But Kavanaugh is not the only one feeling political heat. Democratic Sen. Dianne Feinstein, who learned about the allegations in a letter from the woman dated July 30, is taking fire from Kavanaugh's GOP backers who see the controversy as a character smear and from progressives in her party who said the California senator sat on explosive accusations.

The episode has sent tensions between and inside both parties back to the boiling point over a nomination that could reshape the court for decades. Ill feeling was already deep after Democrats complained the GOP is rushing Kavanaugh through without proper scrutiny by withholding tens of thousands of documents.

The confirmation showdown has also offered key Democrats considering a run for President in 2020 an early forum, with California Sen. Kamala Harris and New Jersey Sen. Cory Booker both winning points with liberal activists, even as they were accused of grandstanding by Republicans.

The accusations against Kavanaugh are being used by liberals to undercut the White House effort to present him as a family man and advocate of women and girls, in part to blunt Democratic accusations that he would vote to overturn the right to an abortion.

Kavanaugh, currently an appeals court judge in Washington, has categorically and unequivocally denied the accusations, and Republicans are furious that his opponents are openly debating them even in the absence of any evidence that they are true. The alleged incident, while Kavanaugh was in high school, was not investigated at the time and there is no sign that the woman reported it to police.

But the pivotal importance of the open Supreme Court seat means the controversy is only going to escalate ahead of an expected Judiciary Committee vote on the Kavanagh nomination next week.

Further fueling the debate, Anita Hill, the attorney who convulsed the 1991 confirmation hearings for Supreme Court Justice Clarence Thomas with sexual assault allegations, issued a statement on Friday night.

"The reluctance of someone to come forward demonstrates that even in the #MeToo era, it remains incredibly difficult to report harassment, abuse or assault by people in power," Hill said.

"The Senate Judiciary Committee should put in place a process that enables anyone with a complaint of this nature to be heard. I have seen firsthand what happens when such a process is weaponized against an accuser, and no one should have to endure that again."

At this stage, there is no indication that Kavanaugh's nomination is under threat, owing to the GOP Senate majority and the huge incentive for Republicans to cement a conservative majority on the nation's top bench.

The woman who made the allegations declined to come forward publicly after making them in a letter that was passed to Feinstein. Advocates say her anonymity should be respected, that she deserves to be heard and the claims must be investigated.

But absent new developments, perhaps on the scale of an on the record, public accusation against Kavanaugh, it is hard to see Republican senators bowing to Democratic pressure to act. Democrats could call for new public or private sessions in the Judiciary Committee to address the allegations. But all of their efforts to shape the confirmation process have been rebuffed by Republicans.

As soon as whispers of the allegations became public on Thursday, the White House accused Democratic Senate Minority Leader Chuck Schumer of using them as an 11th hour delaying tactic to try to slow Kavanaugh's confirmation -- and noted that Feinstein has not previously raised the issue in public.

On Friday, as more and more media outlets reported the allegations, the office of Senate Judiciary Committee Chairman Chuck Grassley released an 11-point statement that was unusually personal in its criticism of Feinstein.

It said that the California senator failed to attend a closed-door session of the committee where sensitive material was discussed, and in which the letter was not referenced.

Grassley's office also sent around a letter signed by 65 women who have known the nominee for 35 years that says that at all times he has "behaved honorably and treated women with respect."

Another key Republican member of the Judiciary Committee, Sen. Orrin Hatch of Utah complained the accusations were unverified and said the judge had submitted to six FBI background checks over the last 25 years that included interviews with families, friends and acquaintances and never revealed any character issues.

"I do not intend to allow Judge Kavanaugh's confirmation to be stalled because of an 11th hour accusation that Democrats did not see fit to raise for over a month," Hatch said in a statement.

Politically, the only threat to Kavanaugh's confirmation appears to lie in the votes of two Republicans, Sen. Susan Collins of Maine and Sen. Lisa Murkowski of Alaska, who have been under fierce pressure from pro-choice advocates to reject him, since he is seen as likely to support cases that could overturn the right to an abortion.

Kavanaugh went ahead with a planned call with Collins that lasted an hour on Friday. The Maine senator's staff declined to give any details of the conversation.

Should the controversy escalate, it could also change the political terrain for red-state Democrats who are under pressure from the party's liberal base to reject Kavanaugh and from their own conservative voters to vote to confirm him.

The political ramifications of the allegations were not confined to questions about Kavanaugh.

Feinstein was left facing an unwelcome new assault from her progressive challenger in California's jungle primary system, state Sen. Kevin de León, who has been framing her as Washington veteran who has lost touch with her voters.

He demanded to know why Feinstein had "waited nearly three months" to hand over the letter to federal authorities and why she had "politely pantomimed her way" through confirmation hearings with no mention of it.

Questions about why Feinstein did not act on information that at the very least could be a seen as a way to slow or disrupt Kavanaugh's nomination are also puzzling Capitol Hill Democrats.

Feinstein's staff tried to stall the fast-building political controversy on Friday afternoon.

A spokesman for the California senator said she took the allegations seriously and thought they should be made public but was constrained by the accuser's wish to remain anonymous.

"It is critical in matters of sexual misconduct to protect the identity of the victim when they wish to remain anonymous, and the senator did so in this case."

The furor over the letter has exposed the awkward spot that Feinstein has faced in the Kavanaugh nomination. In the hearings, she posed pointed legal questions to the nominee on issues such as his attitude towards abortion and interrogations of terror suspects during the Bush administration.

But her interventions lacked the partisan energy of senators like Booker and Harris.

Progressive groups were quick to respond to the allegations about Kavanaugh. The "Rise up for Roe" group of activists said he should "immediately withdraw from consideration."

The Leadership Conference on Civil and Human Rights said the allegation should be taken seriously while respecting the privacy of the woman who made the allegations.

"Once cast, senators cannot take back their vote. They need to be sure they have Kavanaugh's full record before they proceed on his nomination to the Supreme Court," the group's President and CEO, Vanita Gupta, said.