The narrow confirmation of now-Justice Brett Kavanaugh over the weekend marked a major political victory for President Trump – and the beginning of a new battle for Democrats, who are now shifting their message to threaten possible impeachment against the newest high court justice and question the legitimacy of the Supreme Court itself.

After a grueling confirmation fight that included graphic sexual misconduct allegations which the nominee denied, Kavanaugh was confirmed Saturday on 50-48 vote. His ceremonial swearing-in will be held Monday evening.

But as he joins the court, replacing retired Justice Anthony Kennedy, prominent Democrats signal the fight over his seat and the court itself will extend well beyond next month's midterms.

"Now, they want to impeach him. ... It's an insult to the American public," Trump said Monday, still fuming over the confirmation process and predicting Republican candidates would only benefit from the controversy in the midterms.

Democrats, though, maintain the fight is energizing their core. "We will not stop marching, we will not stop fighting," DNC Chairman Tom Perez said in a statement.

Over the weekend, former Attorney General Eric Holder said the court’s legitimacy should be brought into question with the addition of Kavanaugh.

“With the confirmation of Kavanaugh and the process which led to it, (and the treatment of Merrick Garland), the legitimacy of the Supreme Court can justifiably be questioned. The Court must now prove—through its work—that it is worthy of the nation’s trust,” Holder tweeted, referring to former President Barack Obama's Supreme Court nominee whose confirmation process was blocked by Republicans in 2016.

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Sen. Dianne Feinstein, D-Calif., top Democrat on the judiciary committee, also tweeted that confirming Kavanaugh "in the face of credible allegations of sexual assault that were not thoroughly investigated, and his belligerent, partisan performance in last Thursday’s hearing undermines the legitimacy of the Supreme Court."

Some in the media advanced another argument to question the court's legitimacy under its current makeup. Newsweek wrote that Kavanaugh is now the “fourth out of nine justices nominated by a president who did not initially win the popular vote”—referring to President Trump and former Republican President George W. Bush.

Whether the court's legitimacy really comes into question will be seen when major decisions start coming down. More immediately, though, some Democrats are hinting at impeachment efforts should they win the House in November.

Sen. Cory Booker, D-N.J., said the option of impeaching Kavanaugh should not be ruled out and said he would support further investigation into the newest justice.

“If there is conclusory evidence that shows unequivocally that he lied to a Senate committee, that is a crime and he should be held accountable for those criminal acts,” Booker told Yahoo News on Sunday in Iowa, suggesting a probe into whether Kavanaugh perjured himself before the Senate.

He said, though, that Democrats first need to focus on taking back the Senate majority.

“I think that after the dust settles on the night of [November] 6, I think that’s where we start to evaluate … what is the best thing for us to be focusing on in terms of what’s best for America and the American people,” Booker said.

Rep. Jerrold Nadler, D-N.Y., said over the weekend that if the Democrats take back the majority in the House, they will launch a separate investigation into Kavanaugh’s potential perjury and alleged sexual assault.

“It is not something we are eager to do,” Nadler told The New York Times Friday. “But the Senate having failed to do its proper constitutionally mandated job of advise and consent, we are going to have to do something to provide a check and balance, to protect the rule of law and to protect the legitimacy of one of our most important institutions.”

He added: “We have to assure the American people either that it was a fair process and that the new justice did not commit perjury, did not do these terrible things, or reveal that we just don’t know because the investigation was a whitewash.”

Some Democrats even called for considering the impeachment of Justice Clarence Thomas, over sexual harassment allegations he fought off during his 1991 confirmation.

Last month, after an hours-long hearing where both Kavanaugh and one of his accusers, Dr. Christine Blasey Ford, testified, there was a bipartisan call for further investigation into the allegations.

Ford accused Kavanaugh of pinning her down to a bed and trying to remove her clothing at a high school party 36 years ago. She believed it to be an “attempted rape,” according to her legal team. Kavanaugh also faced allegations from Deborah Ramirez, who claimed the Supreme Court nominee exposed himself to her at a dorm party during their freshman year at Yale University; and Julie Swenitck, who claimed Kavanaugh drugged the “punch” at parties and was involved in or present at “gang” and “train” rapes while in high school. Kavanaugh denied all the claims publicly.

The White House ordered a week-long FBI supplemental background investigation into the allegations. The report did not find evidence to corroborate the allegations, though Democrats complained that the probe was limited in scope.

Another point of contention going forward may be Kavanaugh's involvement in a variety of court cases. CNN legal analyst Areva Martin said last week that Kavanaugh should recuse himself from cases involving civil rights, such as gerrymandering.

“Those cases are often brought by political parties, they’re brought by Democrats, so if Judge Kavanaugh believes that this allegation brought by Dr. Ford was somehow orchestrated or engineered by Democratic operatives, how can he be unbiased in a gerrymandering case that’s brought by a Democratic party?” she said on CNN. “His name on the court will always have an asterisk.”

But Harvard Law Professor Alan Dershowitz called that comment “ridiculous.”

“He was confirmed, he will serve on the Supreme Court. He will be judged like the other justices,” Dershowitz said on Fox News' “America’s Newsroom” Monday.

Dershowitz also warned Democrats not to move on impeachment.

“Kavanaugh was not my choice—I’m a liberal Democrat—I would have appointed Merrick Garland again, but the Democrats have to be wise and sensible and just and moral and not violate due process and civil liberties,” Dershowitz said.