The business community and its allies in Congress are pushing back. Employing a rarely used procedural tactic, a coalition of 40 House Republicans joined with Democrats to force a vote on restoring the bank after hard-line conservatives had kept the legislation bottled up despite strong support.

“You have more and more members of Congress, it is becoming more common every day, who are standing up to say, ‘Enough,’ ” said Representative Adam Kinzinger, an Illinois Republican who demanded the bank vote over fierce objections from hard-line conservatives.

Chamber leaders say they intend to “double down” in the 2016 elections and jump in against the hard-right conservative critics when a winnable opportunity arises — exactly what the Tea Party did against Republicans it considered too cozy with the establishment.

“When the Tea Party first formed and they had four or five principles of sound economics, reasonable taxation, etc., etc., I mean who would be opposed to that?” Thomas J. Donohue, the president of the chamber, said at a news media breakfast organized by The Christian Science Monitor. “But it has gone far beyond that to what is lost is the fundamental reality — and that is to govern in a way to create economic growth and create jobs.”