verb

raise objections or show reluctance.

normally she would have accepted the challenge, but she demurred

raise objections,object,take exception,take issue,protest,lodge a protest,cavil,dissent,raise doubts,express doubt,express reluctance,express reservations,express misgivings,be unwilling,be reluctant,balk,hesitate,think twice,hang back,drag one’s heels,refuse,be cagey,boggle,kick up a fuss,kick up a stink