Election Law Blog's Rick Hasen:
The federal challenge to Texas’s strict voter identification law is pending before the entire Fifth Circuit sitting en banc. The Supreme Court set a soft July 20 deadline for a decision—after that the Court has invited plaintiffs to seek immediate relief for this election before the Supreme Court. There’s nothing technically binding about that date, but I expect we will see a decision by then from the Fifth Circuit, and then, whatever happens, I expect an emergency motion to the Supreme Court for whichever side loses.
Meanwhile, the never ending federal district court challenge to Texas’s redistricting remains pending in San Antonio, with a delay that at this point is as inexplicable as it is inexcusable. That case, when decided, will be on a fast-track appeal to the Supreme Court as well, but with any ruling relevant only for elections after 2016.
We are also waiting for other decisions, and one of those big ones is the appeal to the Fourth Circuit of North Carolina’s strict voting laws. That one, too, will likely end up with a request for emergency relief from SCOTUS.
Hasen has predicted that Fifth en banc will deny the photo ID appeal, sending the case on to the Supremes, where a ruling might not come until after November's election, as the court has adjourned for the summer and probably won't render a verdict until long after the first Monday in October. Even an immediate judgment once the Court reconvenes would be very close to the start of early voting (although the change consists of not asking for ID, so your local election judges ought to easily re-adapt to the way Texas conducted elections for hundreds of years previously). Worse, a 4-4 tie would remand back to the Fifth's decision. So the case might have its best chance if it is stalled until there's a ninth justice.
Redistricting is going to wait for 2018, soonest, if it is struck down.
The North Carolina case might also beat Veazey v. Abbott to the Eight (or Nine, depending on how quickly Merrick Garland gets confirmed after a historic delay), and could be the precedent-setter in that event.
So more waiting, but potentially some progress as well.
*Post updated for clarity throughout