A single verse I think speaks volumes about the extent of Christ's atonement is Romans 5:6. Paul writes, "For while we were still helpless, at the right time Christ died for the ungodly" (NASB).Paul tells us here explicitly who Christ died for; the ungodly. Now, many Calvinists claim that Jesus only died for a select few on the cross. He only paid for the sins of the elect. But if this is the case, then Romans 5:6 would indicate that the non-elect aren't ungodly, since Christ died for the ungodly. Or it means, as the Arminian insists, that Christ really did die for the ungodly; namely all those who are at odds with God because of their sin, who Paul identifies as every individual on earth (Romans 3:23).
The only other alternative I could see the Calvinist presenting here is that Paul only means the ungodly among the elect, since Paul says "while we were still helpless." However, this is a tortured reading of this text and in no way follows. "We" clearly means humanity as a whole, but even if it means the specific people Paul is talking to, it doesn't alter the fact that he writes that "Christ died for the ungodly." So if we are to take "we" to mean the elect, it could still read "while [the elect] were still helpless, at the right time Christ died for the ungodly." The article "the" modifies the noun "ungodly" in a way that it causes it to mean ungodly people in general. There really is no other way to read this verse: Christ died for every individual since every individual is ungodly.