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In June, as the House appropriations committee was drafting the annual bill to fund the Treasury Department, the judiciary and a vast mishmash of other agencies, a Kansas Republican known best for skinny-dipping in the Sea of Galilee proposed to dismantle a signature overhaul passed after the financial crisis.

It was adopted after a few minutes of low-key debate, without a recorded vote, really without much notice — until last week. That was when the provision burst into the open and divided Democrats sharply, and it is about to become law as part of a $1.1 trillion spending measure.

How Representative Kevin Yoder’s “push out” provision survived is not, as many have suggested, a tale of dark favors done in back rooms at the last minute. Instead, it is how powerful lobbies work their will, slowly, persistently, bit by bit — in other words, how Washington works.

“It didn’t happen in the dead of night,” said Representative Marcy Kaptur, Democrat of Ohio, who initially forgot she had even spoken against the amendment last summer. “We did the best we could with the votes we had, but we didn’t win.”

The “push out” provision reversed a piece of the 2010 Dodd-Frank law that prohibited banks from trading some of their most exotic financial instruments in units covered by the Federal Deposit Insurance Corporation or the Federal Reserve. The idea was to make sure trades in derivatives, credit-default swaps and other instruments that helped spur the financial crisis of 2008 would not be insured by taxpayers if they went bad.

The nation’s biggest banks have been trying to reverse the provision ever since. A stand-alone bill to repeal the measure was drafted nearly word for word by Citigroup. It passed the House in 2013 by a comfortable 292-122 margin, with 70 Democrats in support.

The banking lobby argues that the provision actually raises financial risk by pushing derivative trading outside the purview of federal regulators. But because such trades would still be made by the same big bank holding companies, big losses would still drain the same capital the banks are required to have to protect federally insured accounts.

“This is a solution in search of a problem,” said Tony Fratto, a former Bush administration official whose Hamilton Place Strategies is consulting for the banks. “I understand the principle they’re trying to achieve. It just makes no sense.”

The Senate ignored the House bill, so bank lobbyists took another route: the appropriations committee. Lawmakers are not supposed to legislate policy changes in spending bills. Those bills are supposed to spend money — perhaps with strings attached, but without broad policy changes.

Mr. Yoder, instead, moved to attach an entire financial reform measure to the annual financial services and general government-spending bill. Aides to the congressman said he was in no way carrying water for Wall Street. Instead, they said, he was looking out for regional and small banks and for farmers caught up in Dodd-Frank regulations.

Large agribusinesses routinely use derivatives to hedge against unexpected fluctuations in crop prices or foreign currencies. Under the new regulations, companies would have to take out loans for farm operations from one bank, strike swap agreements with another financial firm, and provide collateral for both.

At the time, Representative José E. Serrano of New York, the ranking Democrat on the financial services subcommittee of the appropriation committee, questioned how a measure so important could be an amendment to a spending bill.

Ms. Kaptur asked: “I’d like to know, who is really behind this? Who has enough power to bring this before this committee?”

But when it came time for a vote, Democrats did not even bother asking that the names of those in support or opposed be recorded.

Mr. Yoder was an odd choice to offer the amendment. To the broader public, his main claim to fame is a 2012 naked swim in the sea where the Bible says Jesus walked on water, a dip that prompted a public apology as he faced his first re-election campaign.

Securities and investment firms are his largest campaign contributors, but he insisted his interests lay elsewhere.

“This essentially is about creating predictability,” Mr. Yoder said as he laid out the “push out” amendment. “It’s about consumer protection, and financial protection, and lastly it’s about jobs.”

Mr. Serrano formally objected to the measure’s inclusion when the spending bills passed by the House were lumped together last week into one huge bill to finance virtually all of the government. Representative Maxine Waters of California, the ranking Democrat on the House Financial Services Committee, teamed with Representative Nancy Pelosi of California, the House minority leader, to try for one last stand.

But that effort was undercut by the White House, which did not want to risk a government shutdown, and by Senate Democratic leaders, whose focus was elsewhere.

Senior Senate aides said the Democrats beat back other attacks on Dodd-Frank, including more rigorous congressional review of spending by the Consumer Financial Protection Board and efforts to block the designation of financial institutions as “too big to fail.”

Once the Yoder amendment passed the House with bipartisan support, opposition became too difficult, senior Democratic aides said.

Proponents of tougher Wall Street regulation said they saw a precedent in the “push out” experience.

“This attack on Dodd-Frank has been consistent, it has been strategic and it has basically been the kind of work I’ve not seen before,” Ms. Waters said Monday. “I think we’ve learned their strategy.”