The summer primaries will test Democrats’ enthusiasm for electing female executives: In Colorado, Cary Kennedy, a former state treasurer who would be the state’s first female governor, is battling Representative Jared Polis, a multimillionaire who has spent $10.5 million. In Michigan, Gretchen Whitmer, a former state legislative leader, is battling Shri Thanedar, a businessman with no political experience who is pouring millions into his own campaign, and Abdul El-Sayed, a liberal insurgent.
Ms. Whitmer at first struggled to win support from the unions that control much of the state’s Democratic infrastructure. And some officials openly questioned the wisdom of putting forward another woman for governor — Jennifer Granholm ran the state until 2011 — which infuriated female strategists.
And in Florida, Gwen Graham, a former member of Congress whose father was a revered governor and senator, is trailing in the polls to Philip Levine, the wealthy mayor of Miami Beach who has personally financed an enormous advertising blitz.
Faced with the onslaught, Ms. Graham has started more directly invoking her gender.
“Everything I do is through the prism of being a mom,” she said in an ad she began airing last week.
In an interview, Ms. Graham said women “bring a different approach” to politics and mused excitedly about the prospect of her and Ms. Abrams being neighboring governors together.
At the moment, there are just two Democratic women governors: Gina Raimondo of Rhode Island and Kate Brown of Oregon. Ms. Raimondo faces a potentially bruising re-election fight, including a primary challenge from a liberal male opponent, Matt Brown.
Ms. Raimondo said she was hopeful that 2018 would see breakthroughs for women in governorships, but that the country’s political culture had been slow to embrace female executives. Ms. Raimondo said she had counseled a number of women around the country on their decisions to run, and had raised the paucity of female Democratic governors with party donors — many of whom, she said, were unaware of that reality and have historically been more focused on Congress.