Senate Banking Committee Chairman Mike Crapo (R-Idaho), second from left, arrives with Treasury Secretary Steven Mnuchin, right, at the Senate Banking Committee on Jan. 30 on Capitol Hill in Washington. (Susan Walsh/AP)

A plan to scale back post- ­financial-crisis banking rules cleared a key Senate hurdle Tuesday, with more than a third of the Senate Democratic caucus joining united Republicans to move the measure toward passage.

The vote was 67 to 32, well over the 60 votes needed in the closely divided Senate, setting up debate and final passage in coming days.

Days of contentious wrangling on the Senate floor lie ahead, with Sen. Elizabeth Warren (D-Mass.) pledging to deliver speeches in opposition. But the level of bipartisan support Tuesday, with 17 members of the Senate Democratic caucus voting “yes,” suggested the measure will ultimately get the chamber’s approval.

The House would need to approve the legislation as well before it could become law.

If passed, the measure would mark the most significant revision of banking rules since Congress passed a sweeping financial regulatory law in response to the 2008 economic crisis. It is also a rare instance of bipartisan legislating in the Senate, something that has occurred infrequently during the Trump presidency.

Supporters argue that the legislation would bring needed relief to small and regional banks, which say they were treated unfairly under the 2010 financial reform law known as the Dodd-Frank Act.

“This bill is mostly focused on community banks and credit unions. My state’s lost 30 percent” of such institutions, Sen. Mark R. Warner (D-Va.) said ahead of the vote. “That does not help grow the economy, particularly in smaller communities.”

Opponents say the bill would weaken the oversight needed to stave off the type of dangerous lending and investing that brought the U.S. economy to its knees a decade ago.

This bill is “extraordinarily dangerous” for the economy, Warren told reporters Tuesday. “It’s not as if the banks are suffering. They think they can juice their profits if they can get Congress to turn down the regulations.”

The vote is a significant victory for the banking industry, which has seen its fortunes improve under President Trump. He repeatedly promised during the presidential campaign to do a “big number” on Dodd-Frank. The Senate legislation leaves the law’s major provisions intact, though with some parts significantly weakened.

The bill would exempt about two dozen financial companies with assets between $50 billion and $250 billion, including American Express, Ally Financial and Barclays, from the toughest banking regulations. These banks would no longer be labeled “too big to fail” and automatically undergo a yearly stress test to prove they could survive another period of economic turmoil. It also delivers relief to small banks from mortgage and other rules put in place after the financial crisis.

The likelihood that a big bank will fail is small but would be “slightly greater under the legislation,” the Congressional Budget Office said in a report Monday. The report also offered a potential challenge to one of the central arguments of the bill’s supporters: that it will help small banks, not Wall Street behemoths. There is about a 50 percent chance that JPMorgan and Citibank could take advantage of efforts to help other parts of the industry, according to the CBO report.

The measure has exposed a Democratic Party rift over financial regulations that pits liberals such as Warren and top Banking Committee Democrat Sherrod Brown (Ohio) against moderate-leaning Democrats including Sens. Jon Tester (Mont.), Heidi Heitkamp (N.D.) and Joe Donnelly (Ind.).

Tester, Heitkamp and Donnelly are all up for reelection in November in states Trump won by a large margin. Along with Warner, who was one of the lead authors of the original Dodd-Frank bill, Tester, Heitkamp and Donnelly helped negotiate the legislation with Senate Banking Committee Chairman Mike Crapo (R-Idaho). But they said they were not motivated by reelection concerns or the desire to establish a bipartisan voting record.

“I would just tell you that this election has nothing to do with this,” Tester said. “We were working on this five years ago. This has everything to do with access to capital and making sure rural America remains strong moving forward.”

The House passed legislation last year that would repeal larger chunks of the Dodd-Frank rules, so proponents’ biggest challenge may be to reconcile the drastically different bills.

Several of the key Democrats supporting the bill insisted Tuesday that the House must pass their version unchanged or risk ending up with no bill at all. For the House to change the bill “would be folly,” Heitkamp said.

The House typically resists swallowing legislation passed by the Senate without putting its imprint on it. Still, it would be tough for the House to make substantive changes to the Senate version of the bill, said Jaret Seiberg, a financial services analyst for Cowen Washington Research Group.

“That doesn’t mean the House won’t spend a few months trying,” he said. “Yet at the end of the day, the final package will be whatever can get out of the Senate. We don’t see the House being able to make changes.”

Jeffrey Stein contributed to this report.