Why might it be denied? Well, that depends on what happens in the lower courts, but here's a scenario. The liberals win on appeal, and these state laws start getting blocked because they are in conflict with existing Supreme Court precedent (Roe). What if the Court, as a whole, remains uncertain about Roberts and Kavanaugh? The liberal bloc (Ginsburg, Breyer, Kagan and Sotomayor) may oppose granting a writ because they have their temporary victory, and don't want to give the Court a chance to strike down Roe, based on their uncertainty over Roberts and Kavanaugh. The conservatives (Alito, Thomas and Gorsuch) might not trust that both Roberts and Kavanaugh would side with them, and they'd need both to overturn Roe, because without both, they'd just add another case to the list of precedents upholding it. So, if the liberals win on appeal, uncertainty over Roberts and Kavanaugh could lead to a denial of certiorari. Or, maybe Alito, Thomas and Gorsuch stand alone. Three ain't enough for certiorari anyway.
In practical terms, this scenario doesn't rely on there being any uncertainty about Kavanaugh, and really, I don't think there is any. Susan Collins is simply the dumbest person in the Senate. (And in a chamber that includes Bernie Sanders, that's quite an accomplishment!) Roberts is really all that matters here. However, the key to this problem is that Roberts actually has shown some unpredictability, and a reasonable assessment of him is that he'd rather uphold any given abortion restriction on narrow grounds rather than overturn Roe entirely. The issue is that the state laws being passed wouldn't give him that option. So, what's an unpredictable and disingenuous weasel to do? Therein lies the uncertainty. It must, however, cut both ways for this problem to exist. If the liberals know he's on their side, they grant certiorari. If the conservatives know he's on their side, they grant certiorari.
What happens, though, if the conservatives start winning on appeal? It would mean that the lower courts are ignoring precedent, but, um... that can happen. And it would change the calculations. It would mean that the liberals would have to roll the dice, even in the face of uncertainty over Roberts, and grant certiorari. They couldn't let those laws stand, with approval from federal appeals courts.
So, what's going to happen? I don't know. These laws cannot he upheld under existing precedent, but I've pretty much given my opinion of the legal system as it relates to constitutional interpretation before. Judges do whatever the hell they feel like doing, and rationalize it however they want, when they bother. Thanks to that useless idiot, Susan Collins, people are pretending that Kavanaugh is a question mark as it relates to Roe, but come on! There is a sort of question mark: Roberts. I'm not 100% confident that he votes to overturn Roe (although I'd put the number way over 50%), and since the laws are written to force that choice, that turns the matter of granting writs of certiorari into a strategic choice. If nobody on the Court knows for certain what Roberts will do, then the game of granting or denying writs becomes a strategic choice.
So, let's just formalize that quickly, shall we? Because this really is what I do. To simplify it, let's just presume that Ginsburg, Breyer, Kagan and Sotomayor are liberals who want Roe upheld, and Kavanaugh, Gorsuch, Alito and Thomas are conservatives who want it reversed. I'm done with the "uncertainty over Kavanaugh" crap. I've written multiple paragraphs this morning pretending that he's a question mark, and I'm sick of it. He's a conservative, he wants to overturn Roe, and that's all there is to it. Anyone got a problem with that? No? Good. Moving on.
There are two outcomes: Roe is upheld (R), and Roe is struck down (NR). Every liberal has a utility function of Ul(R)>Ul(NR), and every conservative has a utility function of Uc(R)<Uc(NR). What is required for a Justice to grant a writ of certiorari? Let p be an arbitrary liberal's belief about the probability that Roberts will vote to uphold Roe. If a writ is granted, and Roe is upheld, the liberal gets Ul(R), but if Roe is struck down, then the liberal gets Ul(NR). There is a p probability that the liberal gets Ul(R), and a (1-p) probability that the liberal gets Ul(NR). So, our liberal gets the following utility by granting certiorari.:
pUl(R)+(1-p)Ul(NR)
Is granting certiorari rational? Well, that depends on what happens in the absence of a writ. To what do we compare this expression? That depends on the lower courts, which was my previous logic.
So, here's how a rough model would work. Right now, the contest is about holding ground for the liberals. State laws are trying to take ground away from the liberals. If the lower courts let them, then the liberals need to make that up. You would compare that expression to some value, b, where Ul(NR)<Ul(b)<Ul(R). Why? Because abortion will have been effectively banned in some but not all states with indeterminate federal status. It becomes rational to grant certiorari if the following inequality holds.
pUl(R)+(1-p)Ul(NR) > Ul(b)
If the liberals win at the lower level, then you are basically comparing that formula to Ul(R). They aren't the relevant actors. They have no reason to grant certiorari. Instead, it turns to conservatives.
On the conservative side, the formula looks similar. Granting certiorari for a conservative yields the following:
pUc(R)+(1-p)Uc(NR)
What's different is the effect of losing. For conservatives, losing is defaulting to the current status quo, and they'll get another shot. Suppose they grant a writ and lose. So what? They have lost nothing because they default to the current status quo. And pretty soon, Ginsburg will die, and Breyer is 80. Even if Trump doesn't get another appointment this term, he is highly likely to win reelection in 2020, and Roe IS going down. It's just a waiting game. And by that reasoning, the conservatives may as well grant a writ no matter what, and take their chances with Roberts because Alito, Thomas, Gorsuch and Kavanaugh don't give a rat's anal sphincter about precedent, and the next Trump appointment won't either, so the cost to them of Roberts voting to uphold Roe is less than the cost to liberals anyway.
Fundamentally, then, this is an asymmetric process. Time is on the conservatives' side. Roe is going down.
Of course, that won't be much comfort to those who believe that life begins at conception. It logically follows from that belief that abortion is murder. For some reason, liberals don't want to believe that anyone actually holds this belief, hence their befuddlement at the laws that Republicans have been passing, but, you know... try listening once in a while.
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