Republican Sen. Chuck Grassley of Iowa, in his opening statement, quoted from Justice Ginsburg’s eulogy for Justice Scalia in a likely short-lived attempt to appeal to bipartisanship ahead of what will be a contentious week.

“The Senate is now tasked with carrying out perhaps its most solemn duty under the Constitution, as we go through this process, we should heed Justice Ginsburg's words with a shared reverence for the Court, and its part of our constitutional system,” he said.

Gearing up for Democratic attacks, Grassley then said he expects his colleagues will do “anything to derail the confirmation of a Republican nominee" and cautioned them not to allow this hearing to unfold as Justice Brett Kavanaugh’s did.

Expecting her Catholic faith to come up in the hearing, Grassley also reminded everyone of Barrett's rights.

“Let me remind everyone that Article One clearly prohibits religious tests for serving in public office,” Grassley continued. “I expect that you will follow the example of Justice Ginsburg, a nominee should offer no forecast, no hints of how he or she will vote, because that's the role of a judge,” he said, in an apparent reference to the so-called “Ginsburg Rule” con concerning what nominees can say at confirmation hearings.

Setting the tone for Democrats, Ranking Member Sen. Dianne Feinstein, D-Calif., gave a nod to the legacy of the late Justice Ginsburg -- calling her a "standard-bearer for justice” -- before offering a preview of what her Democrats will focus on: Judge Barrett’s views on the Affordable Care Act and what she called the “consequences” of a rushed nomination.

“In filling Judge Ginsburg's seat, the stakes are extraordinarily high for the American people both in the short term and for decades to come. Most importantly, health care coverage, for millions of Americans, is at stake with this nomination,” Feinstein said. “So, over the course of these hearings, my colleagues and I will focus on that subject.”

“We will examine the consequences if, and that's a big " if," Republicans succeed in rushing this nomination through the Senate, before the next president takes office,” she continued, despite Republicans saying they're confident they can get a final vote before Election Day.

The Court is slated to hear oral arguments on the Affordable Care Act, which the Trump administration is seeking to overturn, one week after the election on Nov. 10., raising concern among Democrats on its fate amid a pandemic.

“We can't afford to go back to those days, when Americans could be denied coverage or charged exorbitant amounts. That's what's at stake for many of us, for America, with this nomination,” she said.

Feinstein also quoted Graham from when he previously said that a Supreme Court nominee shouldn't be confirmed when voting is underway.

Graham began his opening statement by reminding his colleagues of the bipartisan Senate support for both the Justice Ruth Bader Ginsburg and Justice Antonin Scalia nominations.

“I don't know what happened between then and now. I guess we can all take some blame,” Graham said. “But I just want to remind everybody, there was a time, in this country, where someone like Ruth Bader Ginsburg was seen by almost everybody as qualified for the position of being on the Supreme Court.”

After he ticked through a list of Judge Barrett’s qualifications, he addressed the matter of the confirmation vote arising in an election year -- a point of contention with Democrats as Republicans prevented a hearing and vote on former President Barack Obama's nomination of Judge Merrick Garland in 2016.

“We're confirming the judge in an election year after the voting has occurred. What will happen is that my Democratic colleagues will say this has never been done and they're right in this regard, I don't think anybody has been confirmed in an election year past July,” Graham said, before getting to what he called his "bottom line."

“The bottom line here is that the Senate is doing its duty constitutionally,” he said. “As to Judge Garland, the opening that occurred with the passing of Justice Scalia, was in the early part of an election year. The primary process had just started.”

Graham also said the hearing will likely not change Barrett's path to the court, noting that Republicans have the votes.

“This is probably not about persuading each other, unless something really dramatic happens. All Republicans will vote yes, and all Democrats will vote no. And that will be the way the breakout of the vote, but the hearing is a chance for Democrats to dig deep into her philosophy, appropriately ask her about the law, somehow she would be different, what's on her mind,” he said.

The four-day confirmation hearing for Judge Barrett is underway in the Senate Judiciary Committee.

Republicans are expected to push for a vote before Election Day as Democrats will try to stop her from turning the court sharply conservative for decades to come.

Committee chairman Sen. Lindsey Graham, R-S.C., is giving his opening statement first, to be followed by Ranking Member Sen. Diane Feinstein, D-Calif. Both appeared in-person and wore masks into the room.

Senators will follow with 10-minute opening statements before Judge Barrett is then introduced, sworn in and gives her opening statement.

Members were given the option of appearing and questioning the witness in person or remotely due to the coronavirus pandemic. Each senator makes their own determination.

The Capitol Hill press pool reported Barrett’s children, in attendance with her Monday, were running down the Capitol Hill hallways and into the hearing room with Barrett, who was wearing a black mask as she took her seat in the committee room.

ABC News’ Trish Turner

The U.S. Supreme Court begins a new term on Monday amidst a raging political battle over an open seat and a high-stakes push by President Donald Trump to have the justices adjudicate a possible contested election.

"Lurking in the background is the possibility this could become the most tumultuous and divisive term since the Supreme Court decided Bush v. Gore 20 years ago," said Irving Gornstein, executive director of the Supreme Court Institute at Georgetown University.

The court will convene as a panel of eight for the first time since the death of Justice Ruth Bader Ginsburg as they await confirmation of Trump nominee Amy Coney Barrett, hearing oral arguments via teleconference that will be livestreamed to the public because of the coronavirus pandemic.

The justices face a fall docket of cases with implications for millions of American families and some of the nation's biggest businesses. They'll address matters of health insurance, use of force by police, military rape claims, religious freedom, grand jury secrecy, robocalls and faith-based foster care.

At the top of the list is a challenge to the Affordable Care Act brought by Texas and 18 Republican-led states backed by the Trump administration to completely invalidate the law, including protections for people with preexisting conditions. It will be argued Nov. 10 and decided by the end of June 2021.

"The stakes of this case have become only higher amidst the global pandemic. One estimate suggests there are 20 million people taking advantage of the exchanges," said University of Chicago law professor Jennifer Nou.

More on other key questions the court will consider this term can be found here.

-ABC News' Devin Dwyer