The battle over Judge Brett Kavanaugh's nomination to the Supreme Court is unlikely to end with his confirmation vote.

Democrats said they won't let go of the sexual assault allegations against Kavanaugh – or accusations he lied about them and other issues before the Senate Judiciary Committee – even if he is elevated to the high court. If they win control of one or both houses of Congress in November, they'll be in a position to continue the fight.

"If he is on the Supreme Court and the Senate hasn't investigated, then the House will have to," Rep. Jerrold Nadler, the top Democrat on the House Judiciary Committee, told ABC's "This Week" on Sunday. "We would have to investigate any credible allegations, certainly of perjury and other things that haven't been properly looked into before."

If Democrats win the House, the New York lawmaker would be in line to chair the committee, giving him not only subpoena power but also the ability to draw up articles of impeachment.

Sen. Sheldon Whitehouse, D-R.I., a member of the Senate Judiciary Committee, made a similar promise: "As soon as Democrats get gavels, we're going to want to get to the bottom of this."

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The battle over Kavanaugh raises the stakes in a midterm election season already inflamed by passions over President Donald Trump.

If confirmed to replace the moderate-to-conservative Justice Anthony Kennedy, Kavanaugh would solidify a conservative majority on the Supreme Court.

The court's October term began Monday with a case involving the Endangered Species Act. Issues of the death penalty, eminent domain and age discrimination are also on the docket.

Some of those cases will be decided by eight judges while Kavanaugh's nomination remains in limbo for at least another week. Last week, Trump ordered a follow-up FBI investigation, which he said would be "limited in scope" to the allegations of sexual assault.

'High crimes and misdemeanors'

The same impeachment power that Congress can use to remove the president can be used against federal judges – including Supreme Court justices.

The process works much the same way: The House votes to impeach by a simple majority vote, sending the question of removal to the Senate. (There's one key difference: Unlike in a presidential impeachment trial, the chief justice does not preside over the impeachment of a judge. That job goes to the vice president, as the president of the Senate.)

A House investigative panel would have the power to compel the testimony of witnesses and gather documents. That investigation could be broader than the sexual harassment allegations, and the constitutional threshold for impeachment – "high crimes and misdemeanors" – isn't limited to criminal wrongdoing.

Some Democrats called for Kavanaugh's impeachment as a judge on the U.S. Court of Appeals for the District of Columbia after his initial confirmation hearing for the Supreme Court. They accused him of lying under oath about his involvement in judicial nominations when he worked as an attorney for President George W. Bush.

Then Christine Blasey Ford went public with allegations that Kavanaugh held her down in the bedroom of a house in Bethesda, Maryland, when she was 15 years old, groped her and attempted to remove her clothes.

Kavanaugh denied those allegations last week in sworn testimony to the Senate. If that denial is proved to be untruthful, it could form the basis for impeachment.

"If that could be established, that, it seems to me, would be the relevant high crime and misdemeanor," said Richard Broughton, who studies impeachment at the University of Detroit Mercy School of Law.

Kavanaugh argued that President Bill Clinton should be impeached for lying about a consensual sexual relationship with intern Monica Lewinsky. Kavanaugh was a staff lawyer for the independent counsel investigating Clinton, Kenneth Starr.

Removal from the Supreme Court requires a two-thirds vote of the Senate – a high bar even if Democrats pick up seats in November. Broughton called that "a tall order."

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"To pierce the intense partisanship and get to two-thirds, it would take far more clarity about the evidence than we have now," Broughton said. "Presumably, that’s what some hope will emerge from the FBI inquiry."

Ford alleged that the sexual assault took place in the early 1980s. That makes it difficult to investigate but wouldn't have any legal bearing on impeachment, said Alan Baron, a Washington attorney.

"There's certainly precedent for it, whether it’s 10 years old or 10 days old," he said.

Baron was the special counsel for the last successful impeachment case in 2010.

U.S. District Judge Thomas Porteous, a Clinton appointee from Louisiana, was convicted in the Senate of four counts, including a charge that he misled the FBI and the Senate during his confirmation process.

The vote on that count was 90-6.

"It wasn't even close," Baron said.

Porteous was the 16th federal judge ever to be impeached and the eighth to be convicted.

Only once has a Supreme Court justice been impeached. Samuel Chase, a Federalist justice appointed by President George Washington, was impeached by a Democratic-Republican House in 1804 for "arbitrary, oppressive, and unjust" decisions on the court.

The Senate declined to remove him from office, setting a precedent that exists to this day. As former Chief Justice William Rehnquist noted in a 1992 book about the case, "it assured the independence of federal judges from congressional oversight of the decisions they made in the cases that came before them."

'Personal bias or prejudice'

In Kavanaugh's impassioned defense before the Senate Judiciary Committee last week, he accused Democrats of a "calculated and orchestrated political hit, fueled with apparent pent-up anger about President Trump and the 2016 election."

Those words could provide fodder for Democratic-aligned groups with cases before his court to ask him to sit out of politically charged issues.

"He revealed himself as a partisan," Sen. Mazie Hirono, D-Hawaii, said on "This Week." "I would think that if I were a Democrat going before him, I’d ask him to recuse himself."

Democrats pressed Kavanaugh to step aside on any cases involving special counsel Robert Mueller's investigation into the Trump campaign. Kavanaugh refused to commit, saying it would undermine the independence of the judiciary.

If he is confirmed, the decision on whether to recuse himself will be his alone.

Federal law requires a federal judge or justice to recuse himself "where he has a personal bias or prejudice concerning a party."

The Supreme Court has never acknowledged that the law applies to its justices, and the law is vague about what constitutes bias.

"The rule is never applied to issues," said Robert Hume, a political scientist at Fordham University who studied Supreme Court recusals. "It has to be prejudice toward particular litigants or parties before the court."

If a justice could be disqualified for having expressed an opinion on an issue, he said, Justice Ruth Bader Ginsburg could never decide any cases involving women's rights, or Justice Clarence Thomas on affirmative action.