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WASHINGTON — House conservatives met Wednesday for the latest installment of their "Conversations with Conservatives" luncheon series, but they took their places on the dais without sampling the Chick-fil-A sandwiches and nuggets on offer.

These days, House conservatives prefer to eat their own.

Republican leaders had scheduled a vote in the chamber for Wednesday on a plan to help people with pre-existing health problems get insurance — part of a broader scheme by Majority Leader Eric Cantor to make Republicans appear to care about the little guy. But the conservatives lunching in the Rayburn House Office Building weren't biting.

One after the other, they vowed to defeat the Republican leaders' bill, which they said was not much better than President Obama's health-care reform:

"I'm going to vote no," said Jim Jordan of Ohio.

"I'm a 'no' on expanding Obamacare," said Tim Huelskamp of Kansas.

"I feel very uncomfortable that we're moving this bill forward," said Marlin Stutzman of Indiana.

"I don't like seeing one big-government Democrat program replaced by a Republican big-government program," said Trey Radel of Florida.

The five other men on the dais Mick Mulvaney (South Carolina), Steve Scalise (Louisiana), Justin Amash (Michigan), Ron DeSantis (Florida) and Raul Labrador (Idaho) — also declared their plans not to back the bill.

The wall of conservative opposition appeared to doom Cantor's warm-and-fuzzy strategy, and party leaders were looking foolish. At the leadership team's morning news conference, The Washington Post's Paul Kane asked Cantor if he had the votes to pass his Helping Sick Americans Now Act.

"Well, listen, this is — that is the whip's purview," Cantor replied, shifting the blame to Majority Whip Kevin McCarthy.

McCarthy had no good answer, so he quoted a movie line. "The first rule of Fight Club: We don't talk about Fight Club," he said.

He didn't need to talk about it; House Republican leaders' actions said it all. At 3:30 p.m., they pulled the bill from consideration rather than let it face certain defeat.

But McCarthy was right about one thing: A fight club is an apt description of the House Republican Caucus at the moment. After November's electoral drubbing, GOP leaders concluded that they needed to move, at least rhetorically, away from their reputation for lowering spending and cutting taxes for the rich.

In February, Cantor proposed a variety of initiatives to move the party "beyond the fiscal debate" and toward the "millions of Americans who just want their life to work again." His proposals included changing comp and flex time, revising worker training, and helping people with pre-existing medical conditions.

But Wednesday's rebellion shows a flaw in the plan. In this case, Democrats opposed the bill because they considered it an attempt to undermine Obamacare. That meant the measure would pass only with near-unanimous Republican support, which seemed unlikely because conservative groups such as the Club for Growth and the Heritage Foundation spinoff Heritage Action opposed it, arguing that it wouldn't repeal Obamacare.

At the luncheon, the nine lawmakers dutifully parroted these arguments. "We're shifting money from one part of Obamacare we don't support to another part of Obamacare we don't support. That's a non-starter for me," Amash said.

Instead, the members demanded another vote on repealing the law — "even if it's just symbolic," as Radel put it. (For those keeping score at home, the attempt would be the 40th.)

As Kane points out, the conservative resistance has made life difficult for Republican leaders this year on everything from hurricane relief to the preservation of Revolutionary War battlefields. That probably presages more trouble for GOP leaders on big issues such as immigration and the budget.

Judging from the reactions at the lunch (coordinated, conveniently enough, by Heritage), Cantor's efforts to humanize his party were about as popular among the conservatives as the cooling nuggets.

"We can talk about flex time, we can talk about bills on Obamacare that are going nowhere," Huelskamp said. "We can talk about messaging. ... But in August, we're going to hit the debt ceiling and we can't avoid that. We're running out of money, and as Republicans, we have to get ready now and talk about the vision of what we have to do to get our country on a 10-year plan to balance the budget."

That budget-cutting theme, he said, "is the kind of message that gets lost in little things."

So helping workers and the sick are "little things"? Cantor can forget warm and fuzzy for now; he has enough trouble just making his colleagues sound humane.

Follow Dana Milbank on Twitter, @Milbank.