WATCHUNG, N.J.—A civic group, formed by a dozen friends after the election, prepared questions for a town-hall meeting hosted this week by U.S. Rep. Leonard Lance, a Republican who has served five terms in this affluent stretch of New Jersey.

Over strawberries and pretzels, members of the Voters of WatchungHills—one of dozens of similar groups that have sprouted in the state—debated how best to challenge Mr. Lance over GOP plans to dismantle the health-care law, and Russia’s alleged interference in the presidential election.

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