Every Supreme Court reporter waits—often in vain and for decades—for a case like AT&T Mobility v. Concepcion. It is a case at the white-hot epicenter of three almost completely inexplicable doctrines: federal preemption, federal arbitration policy, and class action. (I can hear the clamor now from all of you who want me to skip right ahead to the juicy arbitration explanations.) Phrases like contracts of adhesion, exculpatory provisions, ex ante, nonclassable claims, and obstacle preemption fill up the Supreme Court chambers today, like some kind of hideous jargon spill in the Gulf of Mexico. At some point the phrase post ante was uttered, which I don’t think even makes sense. Indeed the only moment in the entire hourlong argument that might have happened in Technicolor came with Justice Stephen Breyer’s baffling metaphor involving a “9,000-foot cow.” And even he seemed to be confused about what that had to do with preemption, arbitration, or cellular telephones.

But sometimes, the most technical, eye-glazing cases can lead to the biggest changes in the legal landscape. Today’s case could profoundly affect anyone in America who has a cell phone contract, a credit card, an employment contract, or aspirations of landing a job at Hooters .

Increasingly, many such contracts, including the cell phone contract at issue in this case, contain arbitration clauses. And the Roberts court has really loved arbitration clauses of late. In this particular case, the arbitration clause between AT&T and its customers provided that both parties to the agreement could bring claims only as individuals, not as part of a class action.

In 2002, Vincent and Liza Concepcion signed up for wireless service that included a free cell phone. They were then charged sales tax on the “free” phone in the amount of $30.32. They filed a class-action suit in federal court claiming that AT&T had fraudulently taxed them on their free phone, and the trial court and the 9th Circuit Court of Appeals each refused to dismiss the case, finding that the arbitration clause was unenforceable and that the federal arbitration statute (the Federal Arbitration Act) did not preempt the California law on unconscionable contracts. Unconscionable contracts tend to be those that are so obviously one-sided as to violate public policy.

(I know, I know: I lost you at “hello.”)

In plain English, the Supreme Court needs to decide whether Corporate America can make ordinary slobs like us, who sign take-it-or-leave-it contracts, give up our right to file class-action suits. And in case you’re wondering why class-action suits matter to us ordinary slobs, consider this: Not a lot of lawyers are willing to take on AT&T for $30.32. Sometimes the only way to police misconduct—particularly small differentials in pay (based on, say, race or gender) or itsy bitsy fraudulent representations—is by pooling litigants together and suing together as a class.

Now you might think this issue sorts itself out on straight liberal/conservative lines, and the amicus briefs filed in the case do not dispel that impression. (The NAACP Legal Defense Fund files a brief on the Concepcions’ side of the case; DIRECTV, the Pacific Legal Foundation, and the U.S. Chamber of Commerce weigh in on AT&T’s side.) * But as oral argument proves, this case is more complicated than that.

Andrew Pincus represents AT&T this morning, and the third sentence out of his mouth is: “Section 2 of the Federal Arbitration Act provides that an arbitration agreement may be held unenforceable under state law only if the state law rule being invoked to invalidate the agreement qualifies as a ground that exists in law or equity for the revocation of any contract.” And with that, every reporter in the room decides to tell their editor just to use a wire story today.

The preemption question is crucial to the case because instead of just fighting over big business vs. clueless customer, we’re also fighting about whether the federal preemption law basically preempts (if I may use that word) the California law that deemed the cell phone agreement “unconscionable.” Pincus appears to lose Justice Antonin Scalia with the claim that states can’t set their own standards for what an “unconscionable contract” might look like. Asks Scalia: “Are we going to sit in judgment? I know you say it has to shock the conscience, but if a state wants to apply a lesser standard of unconscionability, can we strike that down?”

Breyer adds that California seems to have an across-the-board standard for when a contract is unconscionable that applies to both litigation and to arbitration. So why is it that this rule disfavors arbitration? (This is where the 9,000-foot cow in Switzerland makes her appearance. Pincus gamely says something about meadows.)

Justice Sonia Sotomayor is a little quick on the buzzer this morning, which appears to aggravate some of her colleagues, and Justice Elena Kagan proves herself, yet again, to be extremely adept at couching her own questions in the form of Scalia’s questions. As she puts it today, “Now, it may be a good unconscionability doctrine or it may be a bad unconscionability doctrine, but it’s the state’s unconscionability doctrine.”

Deepak Gupta, representing the Concepcions, rises to explain that the Supreme Court should defer to California’s reading of its own common law. But Chief Justice John Roberts interrupts to say that the California courts were discriminating against arbitration agreements in violation of the Federal Arbitration Act. (In a speech in October, Roberts blamed the legal profession for the itty-bitty fine print that comes with pharmaceutical prescriptions and computer agreements.) Justice Samuel Alito appears to agree that arbitration is particularly burdened by the California scheme, which violates the spirit of the federal arbitration law.

Breyer summarizes AT&T’s position: “There are a million customers. I’m faced with a claim for $75 million. I can’t afford that. I’ll settle it, even if I’m right. So if you have your rule, I’m going to be facing these things all the time. I’m not—I’m not going to enter into arbitration agreements. I will take my chances in court.” The nut of AT&T’s argument is that if arbitration is decimated, and class actions are permitted, prices go up for everyone.

Says Gupta: “The state has made a judgment that if you preclude classwide relief, that will gut the state’s substantive consumer protection laws, because people will—in the context of small frauds, not be able to bring those cases.”

What does all this mean for you? For one thing, it means that if you want to meet someone cute at a bar tonight, you’ll do best to avoid discussions of classable claims or obstacle preemption. Perhaps more vitally for your long-term interests, it doesn’t look as though there are too many votes at the high court to do away with the right of consumers to band together to sue the great American manufacturers of fine print.

But I have been wrong in offering such predictions before. Sue me.

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Correction, Nov. 10, 2010: This article originally stated that the NAACP filed a brief in the case. The NAACP Legal Defense Fund is a separate entity. (Return to the corrected sentence.)