(CNN) Major banking reform legislation that sharply divides Democrats advanced Tuesday in the Senate.

Many moderate Democrats -- including several up for re-election in red states -- support the proposed changes to Dodd-Frank, a law enacted in 2010, arguing the tough rules ended up hurting smaller banks. But many progressive Democrats strongly oppose easing regulations for the banks, warning doing so could lead to another financial crisis like the one in 2008, which triggered a deep recession.

The Senate approved a procedural motion on a 67-to-32 vote and will move soon to formal debate on the bill, which could start immediately, if there is cooperation and agreement. If not, formal debate could be held up for up to 30 hours. Seventeen senators who caucus with the Democrats joined with all Republicans who were present, an indication that measure can pass the chamber when a final vote takes place, possibly next week.

"The Senate -- with the support of some Democrats -- is set to start debate on a bill to roll back regulations on the same big banks we bailed out a few years ago. If we lose the final vote next week, we'll be paving the way for the next big crash," said Sen. Elizabeth Warren, a Massachusetts Democrat and a leading liberal who is a vocal critic of changing the law.

Ahead of Tuesday's vote, Warren told reporters she planned to introduce a dozen amendments to the bill to shore up protections for consumers. It's unclear if she will be able to get votes on her proposals.

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