But the 1990 legislation also highlights a basic challenge now facing the party, which the chaos within the House caucus helped bring into public view on Thursday night.

Republicans continue to embrace the no-new-taxes stand as a centerpiece of the party’s identity, even in the face of public opinion that strongly supports tax increases on high incomes. And some Republicans fear that the party’s commitment to prevent tax increases more and more is coming at the expense of those other, older kinds of fiscal responsibility.

“Republicans used to be interested in not running continual rivers of red ink,” said former Representative William Frenzel, a Minnesota Republican who as the ranking member of the House Budget Committee in 1990 helped to negotiate the deficit deal. “If that meant raising taxes a little bit, we always raised taxes a little bit. But nowadays taxes are like leprosy and they can’t be used for anything, and so Republicans have denied themselves any bargaining power.”

The resulting debate has created perhaps the greatest test of the tax stand in the last two decades. Republicans who are willing to accept tax increases as part of a broader deal are pitted against a conservative wing, restocked by the Tea Party wave of 2010, that insists that opposition to tax increases is particularly important at times like these, when the temptation is greatest to avoid spending cuts by asking Americans for just a little more. Many in the antitax camp come from deeply conservative districts and were re-elected by wide margins.

They were not even swayed by Grover Norquist, the activist and arbiter of antitax orthodoxy, who has pushed politicians for the last 25 years to promise that they will not vote to raise taxes, a pledge a vast majority of Congressional Republicans have signed. Mr. Norquist said Mr. Boehner’s proposal was not a tax increase, but he could not convince the generation of politicians he helped create.