To get back to the OP, clearly the context of the passage, the target audience, is believers, for those that are yet dead in sins are not in any way whatsoever constrained in their conscience by the love of God. To pull out the single phrase "that he died for all, then were all dead" and make doctrine from it is a violation of sound hermaneutics.
And what of it anyway? Let's remember that Calvinism does not deny Christ is the Savior of all men. He is the only savior generally speaking, but in particular for the elect. Here we have to carefully examine our doctrine of reprobation. The main of orthodox calvinism teaches that the OPPORTUNITY of salvation is available to all of mankind, but that the ABILITY to obtain that salvation is mercifully provided to His elect. An illustration is a door which represents salvation. God stands at the door, beckoning all of mankind into the door. Since man, of his own will, will not enter the door, God, of His own will and purpose, chooses some in mercy to actively lead into the door by changing their hearts and wills. Now it is important in this analogy to note that God does not stand in the door to BLOCK the entrance, but rather beckons man to enter.
Blocking the door would illustrate active reprobation. Beckoning without further action would illustrate passive reprobation. I think holding to active reporbation can get us into theological corners.
Most of us believe in common grace; and the sufficiency and effeciency of the atonement. It was sufficient in that it was ABLE to procure the salvation of all mankind. In that sense, and only in that sense, Christ's atonement was the atonement for all people. But that's not where the story ends, and it's the rest of the story that arminians don't get - and that is, that the atonement was also EFFICIENT in that it ACTUALLY procured the salvation of the elect, and therefore nothing can be charged against them before God, seeing He has justified them, and if God be for us, who can be against us? I feel a praise-the-Lord coming on!!
