It is not going to be easy to reverse the trend. The 2018 midterm elections showed a steep drop in Republican support among suburban women — typically a core group for the party. The electoral environment was bad enough that one group that advocates more moderate female Republican candidates encouraged those considering a 2018 race to defer, fearing they would be defeated and give up on politics when they could be successful in a different election cycle.

A representative of Emily’s List, the 34-year-old organization dedicated to identifying and endorsing Democratic women who support abortion rights, welcomed the effort by Republicans to elect more women to the still male-dominated Congress.

“We understand the challenges, we understand that it takes work and we are glad they are focused on it,” said Christina Reynolds, a spokeswoman for the organization.

But, she noted, the effort to elect more Republican women faces major obstacles, particularly the party’s strong anti-abortion stance when polls show that most Americans believe access to abortion should remain legal in most cases. That divide is likely to be underscored anew by this week’s passage of a near abortion ban by the Republican-controlled Legislature in Alabama, a measure the Republican governor, Kay Ivey, signed on Wednesday.

“They are going to run into trouble because they are trying to do this in a party that is actively going after women’s rights and has actively dismissed women’s rights,” Ms. Reynolds said.

To illustrate her point, Ms. Reynolds noted that at 13, the number of Republican women in the House is just one greater than the dozen who were serving when Emily’s List was founded in 1985.