WASHINGTON — The Senate advanced legislation Tuesday to roll back some of the safeguards Congress put in place to prevent a repeat of the financial crisis. Enough Democrats supported a procedural vote on the bipartisan bill to show it has a good chance of passage in the coming days.

The move to alter some key aspects of the Dodd-Frank law comes ten years after the financial crisis rocked the nation’s economy. The bill has overwhelming Republican support and enough Democratic backing that it’s expected to gain the 60 votes necessary to clear the Senate. That was reflected in the 67-32 vote Tuesday, with 16 Democrats and one independent voting to move ahead with consideration of the bill.

Several Democratic lawmakers facing tough re-election races this year have broken ranks with Minority Leader Chuck Schumer, D-N.Y. and Sen. Elizabeth Warren, D-Mass.

Sen. Jon Tester, D-Mont., said he was proud to support Dodd-Frank eight years ago, and for the most part, the legislation was successful, but the bill also had unintended consequences, which he said included consolidation in the banking industry and a decline in small business lending. He said local banks in Montana have suffered from regulations specifically designed to rein in risky behavior on Wall Street.

“As a result of complying with these regulations, many of our community bankers are hanging up their hats,” Tester said.

Nonpartisan congressional analysts say the legislation would slightly increase the probability of a big bank failure — prompting a possible taxpayer bailout — or another financial meltdown. The probability of those events is deemed to be small under current law. The new assessment by the Congressional Budget Office estimates the bill would increase federal deficits by $671 million between 2018 and 2027 if it became law.

Sen. Sherrod Brown, D-Ohio, said the drumbeat for derailing Dodd-Frank has been constant. He said Wall Street banks always want “a new exception, or a new, weaker standard, or a new tax break.”

“We know what happens next. It is hubris to think we can gut the rules on these banks again, but avoid the next crisis,” said Brown, the top Democrat on the Senate Banking Committee.

But the bill’s proponents insisted it would bring a needed boost to beleaguered banks outside Wall Street that didn’t engage in the reckless practices that fueled the financial crisis.

“Dodd-Frank’s enormous regulatory burden has been inefficient and unhelpful for financial institutions of all sizes, but it has hit Main Street lenders especially hard,” Senate Majority Leader Mitch McConnell said.

The legislation would increase the threshold at which banks are subject to stricter capital and planning requirements. Lawmakers are intent on easing those rules for midsize and large regional banks, asserting that would boost lending and the economy.

Banks have long complained about the cost of complying with the many requirements of Dodd-Frank. Under the Senate bill, some of the nation’s biggest banks would no longer have to undergo an annual stress test conducted by the Federal Reserve. The test assesses whether a bank has enough capital to survive an economic shock and continue lending. Dozens of banks would also be exempted from making plans called “living wills” that spell out how the bank will sell off assets or be liquidated in a way that won’t create chaos in the financial system.

The Senate legislation increases from $50 billion to $250 billion the threshold at which banks are considered critical to the system. The change would ease regulations on more than two dozen financial companies, including BB&T Corp., Sun Trust Banks Inc. and American Express.

Opponents of the bill argue that the same banks getting regulatory easing through the Senate bill also got about $50 billion in taxpayer-funded bailouts during the financial crisis. Warren said banks got their wish-list in the bill, but consumers got next to nothing.

“This bill was written by big banks to help big banks,” said Warren, who is hoping to offer several amendments to the bill.

The Senate bill emerged from lengthy negotiations between Sen. Mike Crapo, the Republican chairman of the banking committee, and several Democratic members on the committee. Crapo said the Federal Reserve will have the authority to tailor tougher capital and liquidity requirements for individual banks when it believes it’s necessary. For the others, compliance costs should drop.

The bill has 13 Republican and 13 Democratic or independent co-sponsors, a rare level of bipartisanship for substantive legislation in the current Congress. By contrast, the House effort to roll back Dodd-Frank didn’t generate a single Democratic vote in support.

Sen. Bernie Sanders, I-Vt., said the financial sector spent more than $200 million alone on lobbying last year and has donated billions to election campaigns since the 1990s.

“That is why Congress will be spending day after day trying to make life easier for these large financial institutions while at the same time ignoring the needs of working families,” Sanders said.