A sketch artist’s rendering of the Supreme Court’s oral arguments on health reform. (Supreme Court)

“By the end of this week, the justices will likely know, their law clerks will know, and the rest of us have to wait until June,” says Steven Engel, who clerked for Justice Anthony Kennedy from 2000 to 2001.

For the Supreme Court, this week’s oral arguments were, in some ways, the easy part: The justices got to pepper the plaintiffs and defendants with questions about the law. Today, they start digging into a three-month process of writing up a decision on the Affordable Care Act’s constitutionality.

It starts with a conference on Friday, where the justices— and only the justices —likely will discuss this week’s oral arguments. At the end, they will vote — starting with the most senior member of the court, Chief Justice John Roberts, and ending with the most junior, Justice Elena Kagan — on the matter.

“They generally go down the line, and vote,” says John Bash, a former clerk for Justice Antonin Scalia. After that, the senior justice on each side assign who will write the opinion. They go back to their chambers, and the justices begin writing.

Opinions tend to start circulating about a month or six weeks after the conference meeting, according to former clerks, with both the majority opinion and the dissent going to all nine justices. Justices start indicating whether they’ll sign onto a brief, write a concurring opinion or ask for certain changes. The memos tend to be formal, and often brief.

“Let’s say Kagan is writing the majority and Justice Kennedy is joining her,” recalls one former Kennedy clerk. “The simplest memo would read something like, ‘Dear Elena, please join me.’ That means, please join me to your opinion.”

Usually justices stick with the initial position they adopted in the conference. But every now and then, they’ll switch their opinions; the law clerks I spoke with estimated that happened about once every term.

“There’s a 98 percent likely the votes as they’re set down in conference will remain the votes,” says Harry Litman, a former clerk for Justices Kennedy and Thurgood Marshall. “There’s a stronger chance that important chunks of the decision will be modified, softened or revised to account for possible concerns.”

Even though such switches are rare, they can sometimes have dramatic impacts. Yale Law School’s Akhil Reed Amar recalls how Justice Anthony Kennedy switched his vote in a 1992 case, Planned Parenthood v. Casey , providing a fifth vote to uphold Roe v. Wade’s protections of legal abortion.

“Kennedy famously voted, in Casey, to overrule Roe,” Amar said. “And he switched during the writing process and slipped to reaffirm Roe.”

How much lobbying goes on between justices is difficult to say. Many of their deliberations - like the conference meeting - happen behind closed doors, with only the nine justices present. Not even law clerks attend those meetings.

“I didn’t really see it,” said Bash, the former Kennedy Clerk. “I think its uncommon. Justices are very busy people. And you’re also dealing with people who are very experienced in the law, who know what they’re doing. They have 80 cases per term, are here year in and year out. So most of their correspondence is done in conference and writing.”

If it does happen, it’s likely not this week: Litman recounts little lobbying happening prior to the conference, where the justices vote.

“It wouldn’t be unprecedented, on a case like this, for two justices to have a sort of walk in the woods,” he says. “But it would be unlikely to have that take place pre-conference.”

Who, if anyone, might be able to sway a fellow justice? Amar would put his money on the Court’s most junior member, Justice Kagan.

“It happens rarely, but it does happen during the back and forth, and actual drafting of opinions, when you have to write very carefully and figure out the argument,” Amar said. “It happens rarely, but you change your mind. And if anyone can do that, I think Elena can. So I’m really glad Obama put her on the Court.”

All the deliberations are up against a firm deadline: The Court must issue its decision on the Affordable Care Act by the time its term ends in the last week of June. That’s when the rest of the country gets let in on what, for three months, will be one of America’s best kept-secrets.