The Senate started playing catch-up with the House last week when Banking, Housing and Urban Affairs Chairman Chris Dodd (D-Conn.) unveiled his version of a bill that would rewrite the country’s financial rules to avoid a repeat of last year’s economic meltdown.

The legislation is certain to be the vast majority of the committee’s work product for the foreseeable future. The committee has also been working on a handful of other bills, including a measure to prevent banks from charging excessive overdraft fees without customers’ consent and a bill that would impose economic sanctions on Iran.

But regulatory reform remains the top priority, and with opposition to the proposal from the banking industry, some regulators and committee Republicans, significant hurdles remain.

Dodd said markup would begin Thursday for opening statements only, but he does not have a timeline for final passage. He said he expects members of both parties to sign on to the final piece of legislation, despite the fact that the panel’s ranking member, Sen. Richard Shelby (R-Ala.), walked away from the drafting process last month.

“I had hoped today that we’d be standing here with a consensus bill, but I understand that isn’t always possible when you want it to happen,— Dodd said. “But I’m confident and optimistic that will happen.—

Dodd has a long way to go if he wants to win support from the Republican leader. Senate Minority Leader Mitch McConnell (R-Ky.) came out swinging last week, sharply criticizing a proposal he said was not supported by any Republican.

“I don’t think the public is clamoring for us to pass yet another thousand-page bill, and I’m not sure where they’d find the time to do this on the Senate floor, since it’s obvious health care’s going to be the dominant issue for the coming months,— McConnell said.

But some GOP committee members, including Shelby and Sen. Bob Corker (Tenn.), left open the possibility for negotiation despite their concerns.

“We have differences of philosophy and differences of opinion,— Shelby said. “At the end of the day, maybe we can work together and build a real substantive, bipartisan bill, but [Dodd’s plan] is not it.—

Among the non-starters for Republicans is a provision that would establish a new agency to oversee common consumer financial products, such as mortgages and credit cards.

A cornerstone of the administration’s plan, the proposal was a difficult sell in the House Financial Services Committee, where moderate Democrats pushed through a handful of amendments limiting the agency’s authority.

The provision is likely to have a much tougher time making it out of the Banking Committee intact. Although the panel’s more liberal members have championed the creation of the agency, several Democrats have raised concerns.

“There’s still questions I have about it,— Sen. Mark Warner (D-Va.) said.

Republicans have also insisted the measure address the future of mortgage finance giants Fannie Mae and Freddie Mac, which the government took over following the housing market collapse. Dodd has said that although major changes at the government-sponsored enterprises were needed, he wanted to keep that issue separate.

Dodd’s bill would consolidate federal authority over banks and establish a council of regulators with responsibility for monitoring and regulating financial institutions whose failure could pose a risk to the broader economy. It also would create a system for collecting fees from financial institutions after a bank failure — what Dodd called “funeral plans— — to pay for winding down the failed institution.

Those provisions split from other regulatory overhaul plans, including the bill proposed by House Democrats, which would keep the current patchwork system of regulators. Treasury Secretary Timothy Geithner has said the creation of a single regulator is unnecessary and untenable, but he declined to criticize Dodd’s measure last week, saying the legislation “moves us one step closer toward comprehensive financial reform.— Geithner also came out in support of the bill’s funding mechanism for winding down systemically risky institutions after they fail.

There is some general agreement among the committee members on provisions that would consolidate regulation of banks and curb powers of the Federal Reserve.

But the measure is likely to be met with staunch opposition from the Fed, which was protected from such far-reaching proposals in the House bill by Financial Services Chairman Barney Frank (D-Mass.). On the Banking Committee, Sen. Charles Schumer (D-N.Y.) is the most likely to defend the central bank.

Sheila Bair, the powerful chairwoman of the Federal Deposit Insurance Corp. who has fought to protect her turf, is also likely to object to the plan to consolidate her agency’s bank regulatory powers.

Dodd will also have to contend with powerful lobbying groups, including the American Bankers Association and U.S. Chamber of Commerce, which continue to oppose much of the overhaul effort.

The ABA blasted Dodd’s consolidation plan this week, and its president and CEO said the bill “would produce conflicts among regulators, undermine the state-chartered banking system, and impose extensive new regulatory burdens on those banks that had nothing to do with creating the financial crisis.— The Financial Services Committee is on track to meet the administration’s end-of-year goal for completing the measure, a priority second only to sweeping health care legislation. But with health care consuming much of the remaining Senate floor time, the goal for finishing the massive overhaul in that chamber is widely seen as unattainable at this point.

CQ’s Greg Vadala, Phil Mattingly and Benton Ives contributed to this report.