The first complaint, though, was filed September 10 - before the sexual assault allegation came out - and accuses Kavanaugh of lying when he told the Senate Judiciary Committee at a hearing in early September that he hadn't received information stolen from Senate Democrats when he was working in the White House in the early 2000s.
Many polling analysts are forecasting that Democrats will pick up more than the 23 seats needed to win a majority in the House. In each state, Republicans are now just as likely as Democrats to say they are extremely interested - erasing an edge Democrats had in several states last month.
But Democrats see a potential opening in an issue that's dropped off the radar: health care.
Independent pollster Stuart Elway called August's primary results "a wakeup call for the Republicans".
"Hoyer and Pelosi have been measuring the drapes for years now only to come away empty-handed", said Jesse Hunt, spokesman for the National Republican Congressional Committee, the House GOP's campaign arm.
"The biggest challenge is the separating of what's happening in Washington, D.C. from Washington state", she said.
"We won't know until things happen", he told TIME. Garland had been nominated to the Supreme Court by President Barack Obama, but Senate Republicans never acted on the nomination.
"On behalf of our nation, I want to apologize to Brett and the entire Kavanaugh family for the awful pain and suffering you have been forced to endure", Mr Trump said at the jurist's White House swearing-in ceremony.
Kavanaugh was seated on the far right side of the bench Tuesday, next to Justice Elena Kagan, who hired him to teach at Harvard Law School when she was dean.
He said it was unprecedented for a new justice to face such a situation.
"Can we get along?"
He emphasized that Washington voters are known to not vote a straight party line ticket, and he said he trusts voters will continue to vote for person over party. Some even speculated anger over Democrats' treatment of Kavanaugh would spur GOP voters even more.
Re-elected to a seventh term in 2016, Grassley's term runs through 2022.
The other question is whether Trump's personal tax returns would be enough to satisfy the base or would there be a push to also go after Trump's corporate returns, something that could shed more light on the President's business dealings but could also lead to more cries of partisanship. The judges may be forced to conclude "that intervening events have rendered the allegations moot or make remedial action impossible", said Arthur Hellman, an ethics professor at the University of Pittsburgh.