Washington (CNN) Conservative justices and swing vote Justice Anthony Kennedy appeared to side with the Trump administration Wednesday as the Supreme Court heard oral arguments on President Donald Trump's travel ban.

More than a year after Trump caused chaos in the airports by following through on a campaign promise and restricting travel from several Muslim-majority countries, the justices considered the legality of a third version of the original travel ban to decide whether the President ultimately exceeded his authority.

Coming out of oral arguments, the justices wrestled with the travel ban, at times breaking down on ideological lines.

Kennedy's vote could be key, and while he did express some reservation about a candidate's expressions of animus against Muslims during the campaign, he didn't seem to have overall concerns about the President's authority to ban entry, noting that the travel ban could be reviewed every 180 days. Other justices, including Chief Justice John Roberts and Samuel Alito, also highlighted the President's power in this area.

The Trump administration argued forcefully in favor of the travel ban, with Solicitor General Noel Francisco emphasizing "this is not a so-called 'Muslim ban.'"

"It excludes the vast majority of the Muslim world," he told the justices, saying the presidential order was based on neutral criteria and written "after a worldwide multi-agency review."

Alito also noted that the ban only impacts a handful of Muslim-majority countries, at one point stating this does "not look like a Muslim ban."

As Francisco took the podium, liberal justices pounced on the scope of the ban, its indefinite nature and whether it exceeded the President's authority.

Pressed by Justice Sonia Sotomayor about where the President "gets the authority to do more" than what Congress already decided, Francisco said it's up to the executive branch to "set up, to maintain and to constantly improve" the screening system.

Liberal Justice Elena Kagan brought up a hypothetical: what if a president gave strong anti-Semitic statements during his campaign and then issued a proclamation saying no one from Israel could enter the country. She asked if those statements wouldn't be relevant and indicate animus.

Kennedy offered his own hypothetical concern about a candidate who might express hateful statements, and then "takes acts that are consistent with those hateful statements."

"Whatever he said in his campaign is irrelevant?" he asked.

Later, critically, when Neal Katyal, arguing for Hawaii against the ban, came to the podium, Kennedy seemed to express more sympathy for Trump's position. He noted that the travel ban could be examined every 180 days.

And Kennedy asked with skepticism whether the courts should be second guessing the political branches when it comes to national security.

"Your argument is," he said, "that courts have the duty to review whether or not there is such a national contingency -- that's for the courts to do, not the President?" he asked Katyal.

Roberts stressed the White House's national security concerns and asked whether "any type of targeted action" that might impact the Muslim population would give rise to claims of discrimination.

At the end of arguments, Katyal told the justices that if the President disavowed all of his statements, he wouldn't have an issue here.

Katyal told the justices that he told the 9th Circuit exactly that but the President hasn't done that.

Francisco said at the end that Trump has stated this is not a Muslim ban and pointed to specific statements from September 25.

"He has made crystal clear that Muslims in this country are great Americans and there are many, many Muslim countries who love this country and he has praised Islam as one of the great countries of the world," Francisco said.

Ahead of the hearing, a handful of protesters rallied outside the court, holding signs that read "No Muslim Ban Ever," "We will stand together" and "Come for one, face us all."

Several speakers -- including Nihad Awad, the national executive director of the Council on American-Islamic Relations -- also addressed the crowd outside.

"This Constitution, he thinks it's a toy to be played with and to be thrown away when he's bored with its protections," Awad said.

After various iterations of the ban ricocheted through the courts, the Supreme Court agreed last December to allow travel ban 3.0 to go entirely into effect pending appeal.

The version of the ban before the court, signed in September, came after the administration completed a worldwide review as to the vetting procedures of several countries. The ban restricts the entry of noncitizens from seven countries to varying degrees: Iran, North Korea, Syria, Libya, Yemen, Somalia and Venezuela. (Chad has been removed from the list, which Francisco also noted during the hearing)

In court briefs, Katyal relied on a "litany" of statements that Trump made during the campaign and afterward concerning a restriction of Muslims entering the United States and notes that even though the current proclamation was crafted after a review of the entry policies of other governments, it is a "direct descendant of previous bans" covering many of the same countries.

His brief includes some of the President's statements on the campaign trail calling for a "Muslim ban" as well as a retweet of three anti-Muslim propaganda videos he sent on November 29, 2017.

Strong message from court

Both sides say that if the court greenlights the ban it will send a strong message for other presidents and could shed light on how courts should consider statements a president makes during a campaign or on his Twitter feed.

"Nobody denies that the president wields extraordinary power over immigration and national security," said Joshua Matz, who sided with the challengers in a brief filed on behalf of constitutional scholars. "What's at stake here is the president's ability to evade any legal consequence for his own public statements, including those broadcast on a global stage."

Joshua A. Geltzer of Georgetown Law, who also opposes the ban, says the case is about the office of the president, not any one president. "It's about whether our federal courts have a meaningful role to play in enforcing the limits of those authorities, or whether -- as the government argues here -- the courts simply shouldn't be looking at this at all," he said.

Josh Blackman, a law professor at the South Texas College of Law in Houston, believes the justices will find that the travel ban passes legal muster.

"If the court upholds the travel ban on statutory grounds, it will signal that Congress has for decades vested the president with the flexibility to respond to an unforeseeable national security dynamic," he said.

Blackman thinks the court will find that the President has his own inherent constitutional authority to exclude noncitizens and the justices won't hold campaign statements against the President.

"If the Supreme Court rules that the President's actions can be halted based on his campaign statements, courts will be drawn into the unenviable position of serving as fact-checkers for the executive branch," he said.