McCluster said he hadn't even had time to put away the groceries before the woman, who lives alone, let him have it.
"She said, 'I'm praying for you guys. Hopefully you guys can win a game soon,' " he recalled. "I told her we're working hard. She said, 'Well, work harder.'
"I thanked her and told her there's always room for prayer. She told me she had lived in that house for 52 years."
Fan anger has been building all season against the Chiefs, who will be looking for their first home win Sunday when they host Peyton Manning and the Denver Broncos.
Planes have flown over Arrowhead Stadium before games trailing banners that urge the firing of the coach, quarterback and general manager. Last week, thousands of fans wore black to the game to mourn the loss of the season and encourage owner Clark Hunt to clean house.
It sounds as though McCluster's new friend is fully behind the effort, but he took no offense.
"She loves her Chiefs and she wants us to win," he said. "She told us she'd been praying for us. I told her I would relay her message to the whole team to work harder."