The Supreme Court will hear the core of the case against President Barack Obama’s signature health care law today, after appearing Monday to brush aside a technicality that would put off the case until 2015.

With protests and press conferences outside and respectful silence within, the court began the rare three-day argument Monday with anxiety on both sides over the fate of the most far-reaching federal law in decades. In the first 90 minutes of argument, the justices gave few clues as to how they will ultimately rule, but they appeared eager to do so.

Justice Anthony Kennedy — potentially the swing vote in the case — punctured the tension in the room at one point.

“Don’t you want to know the answer?” he asked of how the court would rule on a technical question Monday, to laughs.

“Justice Kennedy, I think we all want to know the answer to a lot of things in this case,” Solicitor General Donald Verrilli Jr. replied.

Today, the court will hear arguments on the central question facing the justices: Can the federal government mandate that individuals buy health insurance coverage?

On Monday, the case attracted a high-profile audience in the packed courtroom, including Attorney General Eric Holder and Health and Human Services Secretary Kathleen Sebelius as well as 10 Members of Congress, including Sens. Richard Blumenthal (D-Conn.), Ron Johnson (R-Wis.) and Jeff Sessions (R-Ala.) and Reps. Robert Andrews (D-N.J.), Marsha Blackburn (R-Tenn.), Diana DeGette (D-Colo.), John Larson (D-Conn.), Joe Pitts (R-Pa.) and Tom Price (R-Ga.) and Del. Donna Christensen (D-Virgin Islands).

Democrats had a largely subdued reaction to the court proceedings, which Blumenthal called a “tone of respectful confidence that the law is on our side.”

Blumenthal said his gut feeling is that the court will uphold the case, but he acknowledged the justices could strike it down. He warned that would be seen as politicizing the court, the way many Democrats view the controversial 2010 campaign finance decision known as Citizens United.

“I think it would be another major step toward undermining the court’s credibility,” he said.

The White House and most Democratic leaders kept their distance from the issue, however.

A Senate Democratic aide acknowledged that Democrats don’t see much benefit in talking about the arcane legal questions surrounding the mandate. “There is no real upside to talking about the law itself if you are not talking about the benefits,” the aide said. The public has moved on, and the law is “not what people want to be talking about,” the aide added.

The aide acknowledged a nervousness among Democrats about the potential for overturning the law — “nobody wants to deal with the consequences” — but felt confident that Democrats would be able to defend their support for the law regardless.

Republicans were eager to trumpet the case, and their opposition to the individual mandate in particular, pointing to polls showing more than 70 percent of people consider the law unconstitutional.

Republican Senators at a press conference outside the court Monday used the opportunity to talk down the law regardless of how the court rules.

“There are lots of things you can do that are constitutional that aren’t the right thing to do,” said Sen. Roy Blunt (Mo.), a member of the GOP leadership team.

They also see the issue as a political win for them in November, as it was in the 2010 midterm elections.

“The principle of the federal government overreach is alive in political halls, whether or not the court legally so concludes,” Sessions said.

Senate Minority Leader Mitch McConnell (R-Ky.) will lead a press conference with state attorneys general fighting the law today after the court arguments, underscoring the GOP’s confidence in its position.

Back in the courtroom, justices on both the liberal and conservative wings of the court appeared to swat away the argument that an 1867 law should apply and effectively delay the case until 2015, when people who fail to buy insurance would be charged a penalty. The 1867 law prohibits people from filing a lawsuit against tax provisions until after they have already paid the tax in question.

While there were few hints at how the justices would look at the broader issues, there were a few sharp moments that crackled in the courtroom. The sharpest exchange hinting at the core of the case came between Justice Samuel Alito and Verrilli.

“Today you are arguing that the penalty is not a tax. Tomorrow you are going to be back and you will be arguing that the penalty is a tax,” Alito said.

Verrilli contended that because Congress did not call the penalty a “tax” in the health care law, it falls outside the 1867 law, which is aimed at preventing lawsuits against federal revenue measures important to keeping the government running. But he argued that the law is nonetheless a “tax penalty” otherwise permissible under the Constitution, which he said was a separate question.

At one point, Verrilli kept calling the penalty a “tax” — correcting himself to “tax penalty” after Justice Stephen Breyer caught him on it — to laughter from the court.

Verrilli essentially argued that the court doesn’t need to reinterpret the 1867 law, just bypass it.

Robert Long, an attorney hired by the court to argue that the 1867 law did apply, warned that opening up an exemption could invite a flood of lawsuits whenever a tax provision is in question.

But several of the justices questioned that idea, positing that a narrow exemption could be granted in this case — as the court did in several other cases from the New Deal era.

Alito also noted concerns that forcing people to wait until after they’ve paid a penalty on the individual mandate puts people in a position of having to disobey the law to make a claim. Long disagreed with that contention, but he later allowed, “I would not argue that this statute is a perfect model of clarity” to chuckles.

DeGette, a lawyer and a prominent backer of the law, acknowledged that the justices face a tricky task in sorting through the tax question. “If they are going to uphold the mandate, they might have to call it a tax,” she acknowledged, and yet, if it is a tax, taking the case now appears to contradict the statute.

“It’s a fine line,” she said.

She said the tax concerns could be the “sleeper issue” but that she expects the court to rule on the broader case and find a way around it.

Otherwise, she surmised, it wouldn’t have taken the case in the first place.

Meredith Shiner contributed to this report.