With a sunny, inviting smile, Senator Katie Britt of Alabama welcomed Americans into her kitchen on Thursday night.

Many soon backed away nervously.

In the Republican Party’s official response to President Biden’s State of the Union address, Ms. Britt delivered a jarring speech that toggled between an increasingly strained cheerfulness and a fierce glare as she gave ominous warnings about illegal immigration.

Ms. Britt, 42, has been seen as a rising Republican star and floated as a possible running mate for former President Donald J. Trump. But in the biggest moment of her fledgling political career, she delivered a tonally uneven speech that was made more unusual by the setting of her own house in Montgomery, Ala., where she sat at her kitchen table and painted a dark picture of an America in decline.

“Our commander in chief is not in command,” Ms. Britt said. “The free world deserves better than a dithering and diminished leader.”

Her comments were in line with messages Republicans have increasingly used to criticize Mr. Biden at the start of the election year, but her 17-minute speech seemed likely to be remembered more for her disconcerting performance. She spoke in grim detail about a child victim of sex trafficking by drug cartels and the recent killing of a Georgia nursing student in which a Venezuelan migrant has been charged.

“That could’ve been my daughter,” Ms. Britt said. “It could’ve been yours.”

Previous State of the Union rebuttals have been delivered from behind a lectern in official settings, but Ms. Britt chose a domestic backdrop, trying to underscore her argument that Mr. Biden represents a threat to prosperity for American families.