In New York, Democrats are mostly focused on unseating six Republican members of the congressional delegation. But for some, merely targeting Republicans is not enough; Mr. Klein’s group, the Independent Democratic Conference, is now fair game because it is viewed as an enabler to Republican rule — helping them control the State Senate even though Democrats hold a numerical majority.
The rising antipathy toward the I.D.C. has led to a tentative agreement to have the renegade group eventually return to the Democratic fold. The condition-laden deal has the blessing of Gov. Andrew M. Cuomo, a Democrat who has been criticized by some — most recently by his new primary opponent, Cynthia Nixon — for not using his influence to force a truce years earlier.
Nonetheless, residual anger over Mr. Trump’s victory, combined with the Democrats’ hopes of flipping Congress in the midterm elections this fall, have invigorated efforts to drive the I.D.C. senators out of office.
A coalition of 60 anti-Trump groups has endorsed five Democratic challengers who will run against members of the I.D.C. in the September primary. The Working Families Party, which often cross-endorses Democratic candidates, has come out in support of seven challengers.
Activists from groups like Progressive Women of Pelham, True Blue NY and Rockland Citizens Action Network have held postcard-writing parties, protests and educational forums to inform the public about the I.D.C.
In some ways, education is the hardest, but most important, part of the movement, activists and the candidates themselves say. Other challenges loom: The I.D.C. members have all the advantages of incumbency, from name recognition to fund-raising.
The I.D.C. was created in 2011 by Mr. Klein, whose district includes parts of the Bronx and Westchester, and a coterie of breakaway Democrats who were dissatisfied with the Senate Democratic leadership. A year later, the group declared its intention to form a bipartisan coalition with Republicans.
Since then, the Republicans have ruled the Senate, while Democrats control the governorship and Assembly. That has left New York out of a club of eight states in which Democrats control both houses of the legislature and the governor’s office.
After Mr. Trump’s victory, Lisa DellAquila, a leader of True Blue NY, created a PowerPoint about the I.D.C. “It’s complicated to understand who they are and what the effect is,” said Ms. DellAquila, a lawyer and stay-at-home mother in Harlem. “I traveled around and made presentations to a couple of people sitting in their living rooms in Riverdale and to big crowds in town halls in Jackson Heights.”
True Blue NY and other groups in the coalition that gave their support to the challengers did so only after the candidates signed a pledge that they would caucus with the mainline Democrats. In recent days, those challengers have started to view themselves as a slate.
“There’s always strength in numbers,” said Alessandra Biaggi, the Democratic candidate for Mr. Klein’s seat who was endorsed by the coalition. “Having the same message amplified in eight different districts is very powerful and important.”
Ms. Biaggi, 31, formerly worked in the counsel’s office for Gov. Andrew M. Cuomo and later was a top official in Hillary Clinton’s presidential campaign. She is also a granddaughter of Mario Biaggi, the Bronx Democratic congressman who went to prison in the 1980s for corruption, but remains a popular figure in the borough.
In her parents’ living room in Pelham Manor, in southern Westchester County, Ms. Biaggi said she adored her grandfather, adding that she was too young at the time of his trial to understand his wrongdoing.
In debating whether to run for Senate, Ms. Biaggi said she was unconcerned about any potential baggage of the Biaggi name. Rather, it was the prospect of a campaign for state office.
“There’s no right time,” she explained. “It’s always going to be inconvenient. But what’s more inconvenient is not having a truly Democratic state legislature to put us on par with California and Oregon. The I.D.C. senators are not who they say they are. They are not true Democrats.”
For their part, the members of the I.D.C. say they have pulled the Senate Republicans to the left and have helped pass progressive legislation, from a $15 minimum wage to raising the age of criminal responsibility.
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