WASHINGTON — The Supreme Court on Monday searched for a middle ground in a case pitting union organizing campaigns against private property rights.

A majority of the justices seemed uneasy with a California regulation that allows union representatives to meet with farmworkers at their worksites for up to three hours a day for as many as 120 days a year. The regulation’s drafters said this was the only practical way to give the workers, who are often poorly educated and hard to locate, a realistic chance to consider joining a union.