One problem for dogmatic universalists (those who don't merely hope all might be saved, they positively believe — from reason and Scripture — that all people will eventually be in heaven) is the problem of ensurance. That is, how does God ensure that all will eventually find their way to heaven. The "ensurance question" can be put like this:
[E] Just how, exactly, does God ensure that all people will eventually be in heaven, thus warranting dogmatic universalism?
There seem to be two options for those "evangelical universalists" who believe you don't get into heaven "no matter what" and that there needs to be some connection to coming through Jesus: Either one gets into heaven by exercise of his libertarian free will or one gets into heaven by exercise of a compatibilist free will.
The first road some universalists take is to posit that compatibilism must be true in order to answer the ensurance question. But a problem arises when we consider that the overwhelming majority of "evangelical universalists" believe that those who don't choose Jesus in this life will go to a terrible hell where they will get another chance to trust in Jesus. To ensure that all of these hellions get into heaven, God will, for some, bring it about that they compatibilistically free trust in Jesus. Here's the problem, and it's taken from their playbook against Calvinism. With Calvinism, it is said that if God can make it that someone compatibilist freely believes in Jesus, why doesn't he do that for everyone, thus saving all from hell?
But at this point the Calvinist gets to use the "I'm rubber you're glue, anything you say bounces of my and sticks to you" argument. It goes like this: If God can bring it about that some will compatibilist freely choose Jesus, why doesn't he bring it about before they die, thus saving them the pain and horrors of hell? If he knows he will eventually have to do this for them, it seems like torture to make them "wait," as it were, when he could have avoided all that pain and torment they would face, and give them immediately to their family members, making their time in heaven that much better (for if you knew your loved one was suffering in hell you couldn't be truly happy until he was released).
The upshot is that universalists who answer [E] by positing compatibilsim should aim their same "injustice guns" against their own position, consigning belief in a temporal hell to the flames. All those who don't libertarian freely choose Jesus in this life God ensures that they compatibilist freely does so. The vast majority of universalists hold to this view, and so the vast majority either need to find that God is a moral monster, or drop their belief in a temporal hell, becoming dogmatic universalists about no one spending any time in hell.
[Addendum: It is illogical to posit libertarianism and compatibilism about the same world. If indeterminism is true, it's a necessary truth, and so compatibilism is false. To avoid this some might claim that God just straight up violates the will and forces hellions to choose Jesus, then hopes that once in heaven they will agree that this is best for them and that believing on Jesus is best for them. Obviously, the same problem arises]
The second road, the harder road, is to keep libertarianism all the way around. On benefit is that it avoids the illogical conjunction of libertarianism and compatibilism. Another benefit is that it keeps a "robust" freedom and eschews the problems inherent in "addendum." A rather glaring defect, however, is that it appears full orbed libertarianism cannot guarantee all will get into heaven. That is, it cannot answer [E].
Philosophers, if anything, are known for coming up with all kinds of unique and creative ways around problems. What looks pretty obvious, viz., that one cannot ensure or guarantee a libertarian free choice, isn't as obvious to some. The idea here is that it is possible for God to guarantee that all will be saved so long as he always leaves the door open for repentance. The illustration here (given by Eric Reitan) is that if you have a box of pennies and you toss the pennies out of the box onto the ground, there's a 50% chance a penny will land heads and a 50% chance a penny will land tails. If heads = heaven and tails = stay in hell, then after the first toss (probably) some pennies go to heaven and some stay in hell. Toss them out again, some may go to heaven, others will stay in hell. The idea is that, mathematically, all will eventually get into heaven, given that the tossing can go on as long as it needs to ensure the result.
The flaw here is that hell is unjust since some people stay in merely by chance. Thus, God could punish a person in hell for one hundred thousand years all because they, by chance, kept landing tails! Whether one gets to be out of hell and enjoying heaven is a matter of luck. So, while [E] might be able to be answered here, it gives us an unjust God. We might want to amend [E] at this point to this,
[E*] Just how, exactly, does God ensure that all people will eventually be in heaven, and do so while remaining just, thus warranting dogmatic universalism?
But if God can just keep people in hell due to arbitrary chance, thus being unjust, why doesn't he just let everyone into heaven without repenting of their sins? Let them in no matter what. So if one wants to keep this pure, random "chancy" indeterminism, he cannot answer [E*], and if he digs in his heels, he just just have God let people into heaven no matter what, Indeed, the latter god seems better than the god who keeps people in hell due to chance.
The upshot of this argument by cases is that, at best, dogmatic universalists need to get rid of their belief in a horrible temporal hell. God ensures all get into heaven before they die. The problem that arises now is that a temporal hell was (partly) posited to get around certain objections like, "Universalism undermines evangelism." But if everyone gets into heaven on the first go-around, whence ariseth the need for evangelism?!