House Democratic leaders plan to move forward this week with campaign finance legislation to roll back a Supreme Court decision that lifted limits on corporate political spending.

The Rules Committee will take up the measure Wednesday with floor action likely Thursday, aides confirmed Tuesday evening. “Leadership is confident we’ll have the votes,” one aide said, pointing to significant progress in rounding up support “in the last 24 hours.”

The bill, officially the DISCLOSE Act, would reinstate some restrictions on corporate and special interest spending in elections.

It ran into trouble last week after Democratic leaders crafted an exemption from its transparency requirement to earn the neutrality of the National Rifle Association. Groups from across the ideological spectrum blasted the deal, and members of both the fiscally conservative Blue Dog Coalition and the Congressional Black Caucus raised their own concerns, forcing leaders to scrap floor consideration planned for last Friday.

Rep. Chris Van Hollen (Md.), the chairman of the Democratic Congressional Campaign Committee and the architect of the package, spent the weekend working the phones to sell the bill to wary colleagues, and the White House threw its weight behind the package this week.

Answering concerns among some Blue Dogs that the House would pass the bill only to see it die in the other chamber, Senate Majority Leader Harry Reid (D-Nev.) and Democratic Conference Vice Chairman Charles Schumer (N.Y.) on Tuesday released a letter in which they pledged to follow through.

David M. Drucker contributed to this report.