COLUMBIA, Mo. — Standing in an airplane hangar in the mid-autumn chill awaiting the arrival of President Trump, Joan Philpott said she was angry and scared. Only Mr. Trump, she said, can solve the problems she worries most about.

“He wants to protect this country, and he wants to keep it safe, and he wants to keep it free of invaders and the caravan and everything else that’s going on,” said Ms. Philpott, 69, a retired respiratory therapist.

Ms. Philpott was one of thousands of women who braved a drizzle for hours to have the chance to cheer Mr. Trump at a rally here on Thursday. While political strategists and public opinion experts agree that Mr. Trump’s greatest electoral weakness is among female voters, here in Columbia and places like it, the president enjoys a herolike status among women who say he is fighting to preserve a way of life threatened by an increasingly liberal Democratic Party.

“He understands why we’re angry,” Ms. Philpott said, “and he wants to fix it.”

As Republican candidates battle to keep their congressional majorities in the midterm elections on Tuesday, Mr. Trump is crisscrossing the country to deliver a closing argument meant to acknowledge — and in many cases stoke — women’s anxieties. At rally after rally, he has said that women “want security,” warning of encroaching immigrants, rising crime and a looming economic downturn if Democrats gain power.