From Vaden v. Discover Bank, No. 07-773, 2009 U.S. 1781 (U.S. Mar. 9, 2009):

[No Federal Jurisdiction from Counterclaim.] A complaint purporting to rest on state law, we have recognized, can be recharacterized as one "arising under" federal law if the law governing the complaint is exclusively federal. See Beneficial Nat. Bank v. Anderson, 539 U.S. 1, 8, 123 S. Ct. 2058, 156 L. Ed. 2d 1 (2003). Under this so-called "complete preemption doctrine," a plaintiff's "state cause of action [may be recast] as a federal claim for relief, making [its] removal [by the defendant] proper on the basis of federal question jurisdiction." 14B Wright & Miller § 3722.1, p. 511. A state-law-based counterclaim, however, even if similarly susceptible to recharacterization, would remain nonremovable. Under our precedent construing § 1331, … counterclaims, even if they rely exclusively on federal substantive law, do not qualify a case for federal-court cognizance.

[Footnote 12] Recharacterization of an asserted state-law claim as in fact a claim arising exclusively under federal law, and therefore removable on the defendant's petition, of course does not mean that the claim cannot remain in state court. There is nothing inappropriate or exceptional, Discover acknowledges, about a state court's entertaining, and applying federal law to, completely preempted claims or counterclaims. ***

.[Jurisdiction Depends on Underlying Dispute.]

The text of § 4 [of the FAA] drives our conclusion that a federal court should determine its jurisdiction by "looking through" a § 4 petition to the parties' underlying substantive controversy. We reiterate § 4's relevant instruction: When one party seeks arbitration pursuant to a written agreement and the other resists, the proponent of arbitration may petition for an order compelling arbitration in

"any United States district court which, save for [the arbitration] agreement, would have jurisdiction under title 28, in a civil action or in admiralty of the subject matter of a suit arising out of the controversy between the parties." 9 U.S.C. § 4.

The phrase "save for [the arbitration] agreement" indicates that the district court should assume the absence of the arbitration agreement and determine whether it "would have jurisdiction under title 28" without it…. Jurisdiction over what? The text of § 4 refers us to "the controversy between the parties." That phrase, the Fourth Circuit said, and we agree, is most straightforwardly read to mean the "substantive conflict between the parties." ***

[Footnote 13] The parties' underlying dispute may or may not be the subject of pending litigation. This explains § 4's use of the conditional "would" and the indefinite "a suit." A party often files a § 4 petition to compel arbitration precisely because it does not want to bring suit and litigate in court. Sometimes, however, a § 4 petition is filed after litigation has commenced. The party seeking to compel arbitration in such cases is typically the defendant, who claims to be aggrieved by the plaintiff's attempt to litigate rather than arbitrate. This case involves the relatively unusual situation in which the party that initiated litigation of the underlying dispute is also the party seeking to compel arbitration.

[Jurisdiction Determined by Entire Controversy, As Pled; Discrete Counterclaim Not Severable for Arbitration.] In holding that Discover properly invoked federal-court jurisdiction, the Fourth Circuit looked beyond Discover's complaint and homed in on Vaden's state-law-based defense and counterclaims. Those responsive pleadings, Discover alleged, and the Fourth Circuit determined, were completely preempted by the FDIA.... The Fourth Circuit, however, misapprehended our decision in Holmes Group. Under the well-pleaded complaint rule, a completely preempted counterclaim remains a counterclaim and thus does not provide a key capable of opening a federal court's door. ***

There is a fundamental flaw in the dissent's analysis: In lieu of focusing on the whole controversy as framed by the parties, the dissent hypothesizes discrete controversies of its own design. As the parties' state-court filings reflect, the originating controversy here concerns Vaden's alleged debt to Discover. Vaden's responsive counterclaims challenging the legality of Discover's charges are a discrete aspect of the whole controversy Discover and Vaden brought to state court. Whether one might imagine a federal-question suit involving the parties' disagreement over Discover's charges is beside the point. The relevant question is whether the whole controversy between the parties — not just a piece broken off from that controversy — is one over which the federal courts would have jurisdiction.

***

It does not suffice to show that a federal question lurks somewhere inside the parties' controversy, or that a defense or counterclaim would arise under federal law. Because the controversy between Discover and Vaden, properly perceived, is not one qualifying for federal-court adjudication, § 4 of the FAA does not empower a federal court to order arbitration of that controversy, in whole or in part.