Senate Democrats on Tuesday appeared to nail down the votes needed to approve a historic overhaul of U.S. financial regulations and set up a final vote by the end of the week.

Senate Democratic Leader Harry Reid scheduled a key vote for Thursday morning after Senator Ben Nelson, one of the chamber's most conservative Democrats, said he would support the bill, which would be the broadest rewrite of the Wall Street rulebook since the Great Depression.

Nelson's support probably gives Democrats the 60 votes they need to clear an expected Republican procedural hurdle in the 100-seat chamber.

If they succeed on Thursday, backers could hold a final vote by Saturday and send the bill to Obama to sign into law.

I believe we have 60 votes, otherwise we wouldn't be going forward, said Democratic Senator Christopher Dodd, one of the chief architects of the bill.

The House of Representatives already has approved the measure and Democrats are eager to get it to Obama's desk.

If signed into law, it would give Democrats an important legislative victory alongside healthcare reform as they try to minimize Republican gains in the November congressional elections.

The Dodd-Frank bill -- named for chief authors Dodd and Representative Barney Frank -- would impose tough new restrictions on the financial industry in an effort to avoid a repeat of the 2007-2009 financial crisis, which touched off a deep recession.

The bill establishes new consumer protections and gives regulators the authority to seize and dismantle large, troubled financial firms. It limits banks' ability to engage in risky trading practices and imposes new regulations on much of the $615 trillion over-the-counter derivatives market.

This reform is good for families, it's good for businesses, it's good for the entire economy and I urge the Senate to act quickly so that I can sign it into law next week, Obama said.

Passage would allow Democrats to capitalize on public disgust with Wall Street, which sucked up hundreds of billions in bailout funds as the financial meltdown pushed the wider economy into a deep recession.

By cleaning up Wall Street, we're going to make sure big bankers can never again gamble away our future, Reid said.

MODERATE REPUBLICANS HELPED SHAPE IT

Three moderate Republicans senators have said they will vote for the bill and have had a hand in shaping it.

Senator Scott Brown won concessions for mutual funds and other financial players in his home state of Massachusetts, while Senator Susan Collins added a provision that will require many banks to set aside more capital to help them ride out future crises.

Republican Senator Olympia Snowe, who won protections for small businesses, said she was disappointed that more Republicans did not support it. On an issue of this kind you would hope to have broader support, she told reporters.

Other Republicans might sign on as well, Dodd said.

Republican Senator Charles Grassley had backed an earlier version, but he is concerned with how the final bill is funded and has not yet decided how to vote, according to an aide.

If Reid cannot find 60 votes this week, he could wait until next week when a Democratic successor is likely to be in place to fill the seat of the late Robert Byrd. West Virginia Governor Joe Manchin is expected to appoint a successor by Friday afternoon, aides said.

Most Republicans have firmly opposed the bill, painting it as an intrusive overreach that fails to address problems in the housing market that spurred the crisis.

There were a number of flaws in it that I think most of my members felt were disappointing and will lead most of my members to oppose, said Senate Republican Leader Mitch McConnell.

(Additional reporting by Thomas Ferraro, Patricia Zengerle and Donna Smith; Editing by Andrea Ricci.)