Facing wide-ranging blowback from an exemption tailored for the National Rifle Association, House Democratic leaders have decided to expand the carve-out from disclosure requirements in a campaign finance measure they are trying to pass this week.

The new standard lowers the membership requirement for outside groups from 1 million members to 500,000. Those groups would still need to have members in 50 states, have existed for 10 years and can accept no more than 15 percent of their funding from corporate or union sources. The broader bill, called the DISCLOSE Act, comes in response to the controversial Supreme Court decision in January that struck down limits on corporate and union spending in elections. The bill would force groups participating in elections to name their top donors, among other changes.

It was not immediately clear which groups would qualify under the new carve-out, though the Sierra Club, with 750,000 members, appears likely to meet the standard. A House Democratic aide said the change was not made with any particular groups in mind. “The number was reduced recognizing that there are groups out there that have a long-standing history of doing grass-roots work. We originally thought some of these groups would be covered, but they weren’t,” the aide said. “This keeps all of the teeth of the bill, but it also sets a uniform standard for groups to meet.”

Leaders plan to take the measure to the Rules Committee on Thursday afternoon and to the floor on Friday.