The U.S. Supreme Court starts a new term today, and while some significant cases are pending - it is still unknown what lies ahead following the death of Justice Ruth Bader Ginsburg.

Senate Republicans are trying to quickly confirm Supreme Court nominee Amy Coney Barrett as the successor for Justice Ginsburg. "I’ve been a leader on getting conservative judges on the Supreme Court, and the best is yet to come," says Sen. Lindsey Graham (R-South Carolina).

A week after the presidential election, the court will hear arguments in a bid by the Trump administration and Republican-led states to overturn the Obama-era health care law. The court is also confronting cases related to the election and to religious rights.

In an email obtained by CNN, Majority Leader Mitch McConnell told his Republican colleagues he needs all of them back on Oct. 19 to ensure a quorum.

However, once again, COVID-19 is a factor. "Think about the health risks involved here.  I mean Dianne Feinstein, the ranking Democrat, is 87 years old.  Chuck Grassley who is on the Judiciary Committee is also in his mid-80s," says CNN Chief Legal Analyst Jeffrey Toobin.

Several senators, including Republicans Thom Tillis, Ron Johnson and Mike Lee, have recently tested positive for the virus.

Democrats are calling on McConnell to put the process on hold. "Even though he has said it's not safe for the Senate to meet in session, but it's OK to have the hearings?" wonders Minority Leader Sen. Chuck Schumer (D-NY).

Some Republicans say things can move forward safely. "I've got a job to do and I'm pressing on," says Sen. Graham.

While some analysts say work on Capitol Hill presents risks.  "There is COVID swirling through the United States Senate, and they are expecting these senators to sit right next to each other, hour after hour, day after day," says Toobin.