The most high-profile primary Tuesday, though, was in Arizona, where just three days after the death of Senator John McCain, Republicans were demonstrating how much the party had drifted from Mr. McCain’s pragmatic style of politics to Mr. Trump’s hard-line nationalism.
Each of the three candidates vying to replace Mr. Flake, who is retiring after a single term, aligned themselves with Mr. Trump.
After asking the president to stay out of the race, Representative Martha McSally, the establishment favorite who will not say how she voted in 2016, sought Mr. Trump’s endorsement earlier this month.
Ms. McSally, one of the first women to fly in combat for the Air Force, was the favorite against the other two Republicans in the race: Maricopa County Joe Arpaio, whom Mr. Trump pardoned last year, and Kelli Ward, a former state senator who garnered nearly 40 percent in a 2016 primary against Mr. McCain and sought to capitalize on his death Monday by saying “political correctness is like a cancer.”
In the governor’s race there, Democrats David Garcia and Steve Farley were running to take on Gov. Doug Ducey, a Republican who may be vulnerable in November.
Mr. Garcia, a former executive at the state education department, has sought to rally progressives, urging them to “imagine no wall in southern Arizona.” Mr. Farley has positioned himself as a moderate, arguing that Democrats can only win in a red-tinted state by presenting themselves as pragmatists.
Oklahoma Republicans were also deciding on their nominee for governor Tuesday. Gov. Mary Fallin, the Republican lame duck, is deeply unpopular and Democrats believe they may be competitive in what is generally a deeply conservative state. Competing in the Republican runoff were former Oklahoma City Mayor Mick Cornett, who hails from the party’s establishment wing, and Tulsa business executive Kevin Stitt.