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As the New York primary approaches, many of Senator Bernie Sanders’s most energetic and enthusiastic supporters are members of the small but influential Working Families Party.

They have donated money, planted signs in their yards, organized rallies and phone banks, and knocked on thousands of doors on behalf of the man who many of them view as a once-in-a-lifetime dream candidate who shares their own left-of-center values.

There is just one hitch: They cannot vote for him on Tuesday.

“It poses a problem, to say the least,” said Jim Mays, 78, a Working Families member who lives in Olivebridge, in Ulster County. He gave a resigned laugh and checked off the ways he has shown his support for Mr. Sanders, including donating small amounts of money, talking up the candidate to his friends and setting out a lawn sign in front of his house.

“Bernie represents the first time we’ve really had an idealistic, leftist candidate in this country in a long time,” Mr. Mays said, adding, “I’ve definitely been waiting for him.”