You can listen to the oral argument here.
With the caveat that one never knows how to read oral argument, and judges can change their minds before issuing an opinion, here are some thoughts:
The judges seemed to believe that the law provided a great burden on the plaintiffs without any good reason put forward by Kansas. Judge Holmes seemed somewhat skeptical of the evidence of the burden proven on the plaintiffs as well as standing on the constitutional claim. He thought some of the burden came from Kansas’s bureaucratic bungling, and not from the law itself. But it was not clear exactly where he stood on the constitutional question.
(The discussion of bureaucratic bungling reminded me of what happened with Pennsylvania’s voter id law. The state was so bad at using its motor vehicle department to get people id, the courts found Pennsylvania inadequately did its job, and Pa. eventually gave up trying to defend and implement its law.)
Importantly, the court focused its argument on the constitutional question, rather than on whether the Kansas law was preempted by the federal NVRA law. There was little discussion of the statutory claim, which suggests to me that plaintiffs are likely to win on at least that claim (which they won on in the court below). There was no discussion, for example, of the trial court’s conclusion that non-citizen voting and voter fraud was a minuscule problem in Kansas, and that DPOC would not be justified then to allow Kansas to enforce its voter qualification grounds.
At the very end, Judge Holmes asked about the difference between striking down the law on constitutional grounds versus NVRA grounds. The state lawyer suggested that striking it down on constitutional grounds, it would cover everyone in Kansas as well as for federal and purely state grounds. An NVRA holding might not cover everyone and would not apply to state elections.
So it may be that the court will decide this on constitutional grounds and not even reach the NVRA issue (if it sides with plaintiffs.) Judges Holmes and Briscoe were on the original panel finding a likely violation of the NVRA.
Note: This post has been updated and corrected.