(CNN) As the Supreme Court justices prepare to take their seats next week to start a new term, they will meet behind closed doors Tuesday to discuss how they'll handle one of the most explosive issues running into the 2020 election : Abortion .

Conservative states, emboldened by a newly solidified conservative majority on the court, are hoping the justices will green-light state restrictions that opponents say could have far-reaching consequences and potentially weaken Supreme Court precedent including the landmark 1973 Roe v. Wade decision that legalized abortion in the US.

As early as this week, the justices could decide whether to take up two cases out of Indiana and Louisiana and they may indicate how they will address a slew of other challenges springing up in conservative states across the county. Additionally, the Court will consider an abortion-related case from Chicago concerning the First Amendment rights of so called "sidewalk counselors" who stand outside abortion clinics hoping to deter women from going inside.

Liberals are looking at the docket fearful of what could come next now that moderate Justice Anthony Kennedy has been replaced by the more conservative Brett Kavanaugh. Justice Ruth Bader Ginsburg, the leading liberal on the Court, said last spring that Kennedy's retirement was the event "of greatest consequence for the current term, and perhaps for many terms ahead."

On the other side of the bench, Justice Clarence Thomas -- who believes that Roe was wrongly decided -- has made clear that he thinks there is no such right in the Constitution. Last term he sent a warning shot to his colleagues about his stance in a separate case. "The Constitution itself is silent on abortion," he wrote.

How the justices deal with the cases before them will send a strong signal about how far and how fast the conservatives on the court want to go.

"The stakes are incredibly high this term," said Jennifer Dalven, director of the ACLU's Reproductive Freedom Project who is behind the challenge in the Indiana case.

Louisiana

The 2014 Louisiana law requires doctors to have admitting privileges at a hospital within 30 miles of the facility where the abortion is performed. It is nearly identical to a Texas law that the Supreme Court struck down in 2016. Back then, Kennedy joined with the liberal justices to rule against the law. Thomas, Chief Justice John Roberts and Justice Samuel Alito were in dissent.

Since that ruling, however, the composition of the Court has changed with the addition of President Donald Trump's picks Kavanaugh and Neil Gorsuch.

Now liberals are worried that the newly comprised court will either undo the Texas ruling or distinguish it from the facts in the Louisiana case and allow the Louisiana law.

The Center for Reproductive Rights, representing an abortion clinic and two Louisiana physicians, argues that if the law is allowed to go into effect is will leave "only one doctor to care for every woman seeking an abortion in the state."

A federal appeals court upheld the law, but Roberts sided last February with his four liberal colleagues to put it on hold until all nine justices could consider whether to take up an appeal.

Critics of the Louisiana law fear that although Roberts took their side on the emergency stay, he may not rule the same way if the full case is before him and the conservatives have the opportunity, through a reasoned opinion, to distinguish the Louisiana law from the 2016 ruling.

Louisiana argues that the law is necessary to provide a higher level of physician competence, but critics say there is no medical justification for the law and it amounts to a veiled attempt to unlawfully restrict abortion.

The case is "the big ticket item when it comes to abortion cases this term," TJ Tu, senior counsel for litigation at the Center for Reproductive Rights, said in an interview. He views the case as "a major test of the Supreme Court's commitment to both the rule of law and its abortion precedent."

"Unless the Supreme Court acts, abortion access is going to be decimated," he said, adding that "if precedent means anything, a law that was unconstitutional in Texas in 2016 has to be unconstitutional in Louisiana today."

Indiana

Justices will also decide whether to take up an Indiana law passed in 2016 that requires a woman to have an ultrasound and be offered the option of viewing the image and hearing the heartbeat at least 18 hours before an abortion.

Critics -- including the ACLU and Planned Parenthood -- note that while the state had already required an ultrasound before abortion (which usually occurred the day of the procedure) the new 18-hour requirement would substantially burden some women because they'd have to travel not once, but twice, to far away health centers that have the necessary equipment. Lower courts blocked the law soon after it went into effect.

"The requirement that women have the ultrasound eighteen hours prior to the abortion places a large barrier to access without any evidence that it serves the intended goal of persuading women to carry a pregnancy to term," wrote a panel of the 7th Circuit Court of Appeals. "Instead, it appears that its only effect is to place barriers between a woman who wishes to exercise her right to an abortion and her ability to do so," the court held.

Indiana is appealing that decision to the Supreme Court arguing that its law "merely combines two pre-existing abortion regulations that are undoubtedly constitutional: an informed-consent waiting period and an ultrasound requirement." Lawyers for the state say the ultrasound "informs a woman's abortion choice and affords her the opportunity to reflect on the information conveyed." They noted that Planned Parenthood "could mitigate the burden" by "simply purchasing additional, less expensive ultrasound machines."

Tom Messner, a senior fellow in legal policy the Charlotte Lozier Institute -- a think tank that opposes abortion, said that his group supports ultrasound laws partly because "that's how people get their information today -- pictures."

"They are very effective to helping people make sure that they make a decision that they're not going to regret later," he added.

Other state cases

The Court is also being asked by the ACLU to take up a Kentucky law that requires a doctor, while performing an ultrasound before an abortion, to describe the procedure, display the ultrasound image and make the fetal heart tones audible to a patient. The law was upheld by the Sixth Circuit Court of Appeals, but the court put its ruling on hold pending appeal.

The court's majority held that because the law "requires the disclosure of truthful, non-misleading, and relevant information about an abortion," it does not violate a doctor's free speech right under the First Amendment.

The ACLU is leading a challenge to the law, saying that it "transforms" standard medical practice into a "pure speech mandate." They say the law requires doctors to display a "graphic description of the ultrasound image (including identifying all visible internal organs) during the ultrasound procedure." And the physician is required to convey the images and sounds to the patient "even if she tries to physically resist them."

At their closed-door conference, the justices will also consider an abortion-related challenge brought by four individuals and two organizations who engage in "sidewalk counseling" with women entering abortion clinics in Chicago.

The petitioners have brought a First Amendment challenge to a regulation that bars a speaker from approaching within 8 feet of another for the purposes of "passing a leaflet or handbill" or "engaging in oral protest, education, or counseling." The so called "bubble zone" ordinance applies within 50 feet of the entrance of an abortion clinic or medical facility.

The city of Chicago argues the restriction is "constitutional" and "narrowly drawn" to regulate the manner and place of speech, not its content.