The most interesting test is coming up in Arizona, where Trump has endorsed Kari Lake, a charismatic former television presenter who is an avid proponent of his baseless election-fraud claims. Lake is leading in polls of the primary, ahead of the favorite of the local Republican establishment and the business community, Karrin Taylor Robson, and Matt Salmon, a former member of the U.S. House who was the Republican nominee for governor in 2002, losing by a whisker to Janet Napolitano.

Ducey, who is term-limited, has said that he “reserves the right” to endorse a candidate in the primary, and Robson, a developer who founded her own land-use strategy firm, would be the logical choice. In 2017, he appointed her to the Arizona Board of Regents, which governs the state’s public universities. Robson was in Nashville this week, according to a local ABC affiliate in Phoenix.

The primary begins earlier than the Aug. 2 date on the calendar suggests. Arizonans vote heavily by mail, and early ballots go out to voters in July. That means the next few weeks are critical, and an endorsement could happen soon.

Will Ducey come off the sidelines? His confidants aren’t saying. If he did so, it would be in his personal capacity. But because he is co-chairman of the R.G.A., his imprimatur would send a signal to donors and other insiders that Robson is the one to back.