Senate Republicans are scrambling to contain the fallout from a sexual assault allegation against Supreme Court nominee Brett Kavanaugh amid escalating calls for he and his accuser to appear before the Senate Judiciary Committee.

GOP leadership is under growing pressure from multiple factions of their caucus, as well as Democrats, to allow Christine Blasey Ford, Kavanaugh’s accuser, to speak before the Senate Judiciary Committee after she decided to go public with her accusation that Kavanaugh sexually assaulted her in the early 1980s.

It's far from clear, however, whether Kavanaugh or Ford will appear before the committee, or whether anything will be done in public.

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Sen. Chuck Grassley Charles (Chuck) Ernest GrassleyThe Hill's 12:30 Report: Ginsburg lies in repose Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy Read: Senate GOP's controversial Biden report MORE (R-Iowa), the chairman of the Judiciary Committee, doubled down early Monday afternoon about his decision to set up staff calls with Kavanaugh and Ford ahead of a scheduled committee vote on Thursday to move forward with the nomination.

Grassley said he was willing to listen to Ford in an “appropriate, precedented and respectful manner.”

“The standard procedure for updates to any nominee’s background investigation file is to conduct separate follow-up calls with relevant parties. In this case, that would entail phone calls with at least Judge Kavanaugh and Dr. Ford. Consistent with that practice, I asked Senator Feinstein’s office yesterday to join me in scheduling these follow-ups,” Grassley said.

He added that Democrats were so far refusing to take part in the call but it’s “a necessary step in evaluating these claims, I’ll continue working to set them up.”

A public hearing carries obvious risks for Republicans in the "Me Too" era that has toppled high-profile figures both on and off Capitol Hill.

It would have echoes of the Anita Hill hearings, in which a former colleague of Supreme Court Justice Clarence Thomas testified about allegations of sexual harassment. Thomas was confirmed despite Hill’s testimony, which was carried live on television at the time.

A new public hearing where Ford would detail her charges and be questioned by senators would spark a media frenzy less than two months before a midterm election where control of Congress hangs in the balance.

Both parties are conscious of the role that women voters will play in the midterms. Polls suggest woman are breaking against the GOP and President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE, who has faced accusations himself of sexual harassment and assault.

Republicans on Monday seemed to be lining up behind Grassley in arguing there should be no new public hearing.

Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (Texas), the No. 2 Senate Republican, said that Democrats had “egregiously mishandled” the allegation from Ford by not making it public earlier. He said Republicans shouldn’t make a similar mistake by holding a new hearing.

“If Democrats reject the committee handling this swiftly and in a bipartisan way through regular order, then it’s clear that their only intention is to smear Judge Kavanaugh and derail his nomination,” Cornyn said.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) has yet to comment on the allegations since they surfaced late last week.

“Professor Ford and Judge Kavanaugh should both testify under oath before the Judiciary Committee,” Collins said in a tweet.

Sen. Lisa Murkowski Lisa Ann MurkowskiClub for Growth to spend million in ads for Trump Supreme Court nominee Pebble Mine CEO resigns over secretly recorded comments about government officials Maryland's GOP governor says Republicans shouldn't rush SCOTUS vote before election MORE (R-Alaska), who voted against an ObamaCare repeal bill last summer along with Collins, told CNN late Sunday night that the Judiciary Committee “might” need to consider delaying a Thursday vote.

Republicans can only afford to lose one GOP senator before they need to lean on Democrats to confirm Kavanaugh. Democratic Sens. Joe Manchin Joseph (Joe) ManchinManchin defends Supreme Court candidate Barrett: 'It's awful to bring in religion' The Hill's Morning Report - Sponsored by Facebook - Trump, GOP allies prepare for SCOTUS nomination this week Trump meets with potential Supreme Court pick Amy Coney Barrett at White House MORE (W.Va.), Heidi Heitkamp Mary (Heidi) Kathryn HeitkampHarris faces pivotal moment with Supreme Court battle Centrists, progressives rally around Harris pick for VP 70 former senators propose bipartisan caucus for incumbents MORE (N.D.) and Joe Donnelly Joseph (Joe) Simon DonnellyHarris faces pivotal moment with Supreme Court battle Trump meets with potential Supreme Court pick Amy Coney Barrett at White House Names to watch as Trump picks Ginsburg replacement on Supreme Court MORE (Ind.) were once considered potential “yes” votes, but the sexual assault allegation has thrown Kavanaugh’s ability to win over Democrats into question.

Donnelly on Monday called for the Judiciary Committee to delay its vote, while Heitkamp said Ford should be allowed to testify and that the panel should give time for her allegation to be investigated.

Collins and Murkowski aren’t the only Republicans arguing that Ford should be allowed to testify or that the Judiciary Committee should slow down, either, underscoring the tenuous footing Kavanaugh’s nomination is on.

Sen. Ron Johnson Ronald (Ron) Harold JohnsonThe Hill's 12:30 Report: Ginsburg lies in repose CHC leaders urge Senate to oppose Chad Wolf nomination Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy MORE (R-Wis.) told a Wisconsin radio station on Monday that Ford “is willing to come forward and tell her story and we should listen to her."

Republicans initially signaled that they thought they could move Kavanaugh’s nomination through the Judiciary Committee this week, and the Senate floor by the end of the month, when the allegations were anonymous.

But Ford’s lawyer said on Monday that she is willing to testify before the Judiciary Committee after she spoke with The Washington Post on Sunday. Ford told the Post that at a party when both she and Kavanaugh were in high school Kavanaugh pinned her to a bed at a party and attempted to take her clothes off.

And Kavanaugh subsequently released a statement on Monday denying wrongdoing but saying he was willing to speak with the Judiciary Committee.

Sen. Roy Blunt Roy Dean BluntSocial media platforms put muscle into National Voter Registration Day Senate GOP faces pivotal moment on pick for Supreme Court This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (R-Mo.) became the first member of leadership on Monday to say Ford’s allegation should be looked into before the Judiciary Committee moves forward.

“These are serious allegations that need to be looked at closely by the committee before any other action is taken,” Blunt said in a statement.

In addition to Blunt, GOP Sens. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (Ariz.) and Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (Tenn.) have both called for the committee work to be paused until senators are able to talk to Ford.

“For me, we can’t vote until we hear more,” Flake told the Post.

Flake’s stance could be particularly problematic to Kavanaugh’s nomination. Republicans hold a one-seat majority on the Judiciary Committee, meaning if he sides with Democrats in voting “no,” Kavanaugh wouldn’t have the majority needed to get a favorable recommendation from the panel.

Republicans could try to use procedural maneuvers to get Kavanaugh out of the Judiciary Committee without a favorable vote, but it would raise new questions about his ability to get confirmed by the full Senate.

And it would invite, potentially inevitable, comparisons to the confirmation fight around Thomas.

Progressive groups are calling on the White House to withdraw Kavanaugh’s nomination, which would allow them to avoid a second hearing but is something the administration has said it will not do as it stands by Kavanaugh.

The move would allow Republicans to try to get a second Supreme Court nominee confirmed in the lame duck. It takes Supreme Court nominees roughly 67 days from the time they are nominated until they get a vote.

That would mean the administration would need to withdraw Kavanaugh and nominate someone else quickly if they wanted a justice in place by the end of the year. Democrats have a narrow path to retaking the Senate in January, which could prevent Trump from filling the seat.

Adam Jentleson, an aide for former Senate Majority Leader Harry Reid Harry Mason ReidThe Supreme Court vacancy — yet another congressional food fight Trump seeks to turn around campaign with Supreme Court fight On The Trail: Battle over Ginsburg replacement threatens to break Senate MORE (D-Nev.), floated that moderate GOP senators could urge the White House to withdraw Kavanaugh in exchange for supporting whoever they send up

“To avoid spiking his nomination, Collins & Murkowski could urge the WH to get Kavanaugh to withdraw & nominate someone like Amy Coney Barrett on the promise that they’ll vote to confirm her in lame duck. Of course, that’s after the election & the world could look very different,” Jentleson wrote in a tweet.