Republicans hold a slim majority in the US Senate, the body that confirms Supreme Court judges, making Judge Barrett's nomination very likely to pass.
Democrats have criticised the rushed process as "reckless" and a "sham", amid a coronavirus pandemic that has killed 215,000 people in the US.
They have also accused Republicans of hypocrisy. In March 2016, when Mr Obama, a Democrat, put forward a nominee to fill a spot on the court, the Senate Republicans refused to hold hearings, arguing the decision should not be made in an election year.
What's in store for Tuesday's hearing?
Tuesday is the first of two days of direct questioning for Judge Barrett from senators on the deeply divided Senate Judiciary Committee.
It follows day one of hearings on Monday, in which she explained her legal philosophy and qualifications for the lifetime position on America's top court.
Democratic senators are likely to scrutinise her conservative views and decisions she has delivered as a judge on the Seventh Circuit Court of Appeals. Much of her record could be seen to be in opposition to the philosophy of the late Justice Ginsburg.
Healthcare is high up the agenda, amid the possibility that she could be a deciding vote to strike down reforms enacted by former President Obama, providing health insurance to millions of Americans.
The top Democrat on the committee, Senator Dianne Feinstein, argued on Monday that "Americans stand to lose the benefits that the ACA [Affordable Care Act] provides" if Judge Barrett is on the top court, when it hears a case against the public health insurance scheme next month.
"It's beyond ironic that this administration, which has failed to respond to this pandemic, is rushing through a judge they believe will vote to strip away health protections," Democratic Senator Chris Coons said.
Judge Barrett has in the past criticised a 2012 Supreme Court ruling upholding the ACA.
Republicans on the committee however praised Judge Barrett and defended the legitimacy of confirming the judge.
The hearings, lasting four days, are the key step before a full Senate vote on the nomination.
What did Judge Barrett say on Monday?
"I believe Americans of all backgrounds deserve an independent Supreme Court that interprets our constitution and laws as they are written," the 48-year-old jurist, who is deeply religious and has conservative views on abortion, told senators on Monday.
Judge Barrett argued that elected politicians make "policy decisions and value judgments", not Supreme Court justices.
"In every case, I have carefully considered the arguments presented by the parties, discussed the issues with my colleagues on the court, and done my utmost to reach the result required by the law, whatever my own preferences might be," she said.
Who is Amy Coney Barrett?
favoured by social conservatives due to record on issues like abortion and gay marriage
a devout Catholic but says her faith does not influence her legal opinion
is an originalist, which means interpreting US Constitution as authors intended, not moving with the times
lives in Indiana, has seven children including two adopted from Haiti
What's the confirmation process?
After the hearings end, any committee member can require an additional week before the formal panel vote on whether to present the nomination for confirmation before the full Senate. It is not clear if the members will be able to vote remotely.
If she passes the committee stage, the full Senate will vote to confirm or reject Judge Barrett's nomination.
Republicans already appear to have the 51 votes needed to get Judge Barrett confirmed.
Senate majority leader Mitch McConnell has vowed to hold a confirmation vote before the presidential election.
Barring a surprise, Democrats seem to have few options to prevent her from gliding through the Senate to the Supreme Court bench.