Washington (CNN) Senate Judiciary Chairman Chuck Grassley said his committee's hearing with Brett Kavanaugh and Christine Blasey Ford would go forward as planned Thursday even as new allegations surfaced against President Donald Trump's embattled Supreme Court nominee .

Grassley, an Iowa Republican, told reporters Wednesday that while they are investigating the new allegation, there will not be a delay of the prescheduled hearing, saying "tomorrow is very important." A Grassley spokesman later reiterated the hearing will go on as scheduled.

The latest allegation comes from a woman named Julie Swetnick, who attended Gaithersburg High School in Maryland. Swetnick says she attended "well over ten" parties where Kavanaugh was present and saw him "drink excessively at many of these parties and engage in abusive and physically aggressive behavior towards girls, including pressing girls against him without their consent, 'grinding' against girls and attempting to remove or shift girls' clothing to expose private body parts." Ford has accused Kavanaugh of sexual and physical assault during their high school years at a party in the early 1980s.

Kavanaugh has denied all allegations against him, including those of Ford and Swetnick.

One the chamber's most watched Republicans, retiring Sen. Jeff Flake of Arizona, took to the Senate floor after the latest allegations to offer an apology on behalf of the US Senate to Kavanaugh and Ford, as well as rebuke Trump and both Republican and Democrat lawmakers, for what he saw as an over politicization of the confirmation process.

"I must also say that separate and apart from this nomination and the facts that pertain to it, I do not believe that a claim of sexual assault is invalid because a 15-year-old girl didn't promptly report the assault to authorities, as the President of the United States said just two days ago," Flake said.

Flake, a member of the Senate Judiciary Committee, also said warned that his fellow panel members may "have to be prepared for the possibility, indeed the likelihood, that there will be no definitive answers to the very large questions before us" following Thursday's hearing.

Republicans keeping timeline so far

Republican Sen. John Cornyn, who as majority whip is the second ranking GOP member in the chamber, echoed the message from Grassley that the Thursday hearing with Ford and Kavanaugh will take place as scheduled.

"These most recent allegations just don't have anything to do with Dr. Ford," Cornyn said. "We have committed to hearing from her and that's what we'll be doing tomorrow."

Cornyn indicated that he wants the Senate vetting process to move forward as quickly as possible, saying that he believes, "the longer this nomination strings out there, the more you're going to get reckless accusations that have no basis in fact."

Cornyn also said GOP leaders are still pushing toward a vote in the full Senate Tuesday, following a committee vote scheduled for Friday morning.

"We are not going to vote on confirmation until Tuesday," Cornyn said. "I suspect that that is plenty of time for that interview to take place. And I suspect that the longer that this hangs out there, the more, the more accusations will occur. Including those like Miss (Deborah) Ramirez, which by her own terms she is not sure if she correctly identified Brett Kavanaugh or not."

Cornyn was referencing allegations published in The New Yorker where Ramirez accused Kavanaugh of inappropriate sexual behavior in the 1980s when they were in college. Kavanaugh denied those allegations.

Sen. Lindsey Graham, a South Carolina Republican who sits on the Judiciary committee with Cornyn and Grassley, said he does not believe Kavanaugh is a serial rapist. When asked if Kavanaugh's confirmation process in the Senate should be delayed or halted to investigate the new allegations, Graham responded, "absolutely not."

In a separate statement, Graham stated, "This is outrageous, internally inconsistent, and I hope the US Senate will see this for the smear campaign that it is."

Republican Sen. Orrin Hatch, who also sits on the Senate Judiciary Committee, told reporters Wednesday, "We can look at these allegations and we can determine whether they are valid or whether they are serious or not. But it's awfully odd that they're suddenly coming up at the last seconds of this even after we've had hearings and all kinds of other things. You have to be very suspect of this kind of stuff. There are people out there that you can't trust."

Hatch, who is one of three senators who sits on the committee now as well as during the 1991 Anita Hill hearing, added, "I don't think it's fair to Brett Kavanaugh, I don't think it's fair to our system, I don't think it's fair to the process. I don't think we should put up with it to be honest with you. I have a lot of suspicions."

How Democrats are responding

Democratic lawmakers on the Senate Judiciary committee seized on the new allegation on Wednesday to renew their calls for an FBI investigation, which the White House and Senate Republicans have said is not merited.

In a letter to the President on Wednesday, all 10 Democratic senators on the panel called on Trump to either "immediately withdraw" the Kavanaugh nomination "or direct the FBI to re-open its background investigation and thoroughly examine the multiple allegations" that the nominee now faces.

Senate Minority Leader Chuck Schumer responded to the latest allegations by calling on Republicans to "immediately suspend the proceedings related" to the nomination and saying that he believes Kavanaugh "should withdraw from consideration."

"Republicans need to immediately suspend the proceedings related to Judge Kavanaugh's nomination, and the president must order the FBI to reopen the background check investigation," the New York Democrat said in a statement.

He added, "I strongly believe Judge Kavanaugh should withdraw from consideration. If he will not, at the very least, the hearing and vote should be postponed while the FBI investigates all of these allegations. If our Republican colleagues proceed without an investigation, it would be a travesty for the honor of the Supreme Court and our country."