Certainly for these one major problem is that they are set up on the belief that God must give everyone an equal shot at salvation - that it's unfair of God not to equip everyone to accept Christ. I suspect that some bristle at the idea of the "unfairness" of unconditional election, but also agree that without the prior action of God's spirit none will see their need and humbly submit to the Lord. Thus they set up some sort of system in which God grants everyone the eyes to see - and some don't use them, and are therefore lost.
I just got the book shown at above, God's Glory in Salvation Through Judgment, by James M. Hamilton, Jr., and think there may be something in it that is related to why some have issues with the punishment of sinners. That is, I think what such folks have an issue with may be related to the subject matter of the book. It looks like a very good read - a biblical theology centered on the idea that salvation comes to individuals ultimately through judgment. I'm very much looking forward to it - and suggest you might want to pick it up as a new read for the winter.
I suspect that for some the issue is very deeply wrapped up in something of a different problem - that they cannot see God as glorified in the damnation of any. I *think* perhaps the receipt of this book has led me to these thoughts (but I am not certain). That is, my hypothetical objector has no problem agreeing that sin is deadly and deserves punishment - but I wonder if they see God less as a righteous judge justly condemning the sinner, and more as their father, saying "I hate to do this, but I'm going to have to spank you, son." Punishment of sin, to them, would be something God would really rather avoid, and in some sense almost does despite His unwillingness to do it. Certainly for someone approaching the issue with this mindset, the punishment of sinners would not be something that brings God glory. For them, God's glory would come only through redeeming people through Christ. They would seem to be blind to the fact that God is also glorified in judgment and condemnation of the rebel.
There are all sorts of issues with this, of course, but I wonder if I'm onto something....