After hearing oral arguments on what could be one of the most important abortion cases decided by the U.S. Supreme Court in decades, NPR's Nina Totenberg says that the only thing that is certain is that Justice Anthony Kennedy will cast the deciding vote.

As expected, Nina says, the three conservatives and four liberals on the court stuck to their positions for and against a Texas law that puts restrictions on abortions.

As Nina reported earlier today, the law requires all abortions — either surgical or medical, meaning with pills — to be done in ambulatory surgical centers. The law also requires doctors to have admitting privileges at a hospital within 30 miles of the clinic. The question before the court is whether these restrictions impose an "undue burden" on a woman's constitutional right to end a pregnancy.

Nina says that Kennedy floated the idea of perhaps punting on this case and sending it back to a lower court to gather more evidence on how the law has affected access to abortion in the state.

"The question is really are they going to decide this? Are they going to uphold the privileges requirement? Are they going to uphold the surgical center requirement? And the answer to that I do not know," Nina says.

Opponents of the Texas Omnibus Abortion Bill, known as HB 2, argued that since the law was passed in Texas the number of clinics that perform abortion dwindled from 41 to 19.

Nina says that the conservative justices wanted to know how opponents of this law knew that those clinics had shuttered because of the law.

"The solicitor general for example, noted that for at least seven of these clinics, they literally couldn't comply with the law, that in order to comply they would exceed the footprint of the land that the clinic is on," Nina says. "It was quite a passionate battle between the court's liberals and that includes the three women on the court, who were very vociferous, and the court's conservatives who would really love not be ruling on this at all. And I don't know where it's going."

Of course, another question is whether the court could end up at a 4-4 tie because of the death of Justice Antonin Scalia. Nina says that doesn't look likely, but if it did, it would mean that the Fifth Circuit ruling, which largely upheld the law, would stand. The ruling, however, would only be valid in the states under the Fifth Circuit's jurisdiction and a tie would lead to a patchwork of laws across the country.

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