That’s everybody’s family.” In Kansas City, Kan., dozens of protesters gathered outside the office of Representative Kevin Yoder, another Republican House member in a district won by Mrs. Clinton, as the House voted on Thursday. “I feel a pivot,” said Debra Caplan, a founder of NJ-11th for Change, a group that for months has turned out hundreds of protesters each week outside the New Jersey offices of Representative Rodney Frelinghuysen, the powerful chairman of the House Appropriations Committee. Protesters are promising fireworks for those who plan to have sessions — including Representative Tom MacArthur of New Jersey, a moderate who negotiated an amendment that secured the support of members of the conservative Freedom Caucus by weakening insurance regulations, including protections for people with pre-existing conditions. And they are looking ahead to the midterm elections next year, vowing to punish Republican House members who voted in favor of the American Health Care Act, the formal name for the bill. With the controversial Republican health bill heading to the Senate, organizers of opposition groups say they plan to bird-dog Mr. Gardner’s whereabouts and show up at his events, buying seats at fund-raisers if necessary.