House Democratic leaders have brokered a deal to exempt the National Rifle Association from legislation to counteract a controversial Supreme Court decision relaxing campaign finance rules.

The compromise marks a major breakthrough for the bill, because the gun lobby’s opposition was hamstringing Democratic efforts to round up majority support. But other heavyweight political groups important to endangered Democrats remained opposed — namely, the U.S. Chamber of Commerce and the National Right to Life Committee.

And powerhouse liberal groups such as the AFL-CIO and the Sierra Club have yet to sign off, pending fixes they said they are still negotiating with leaders.

Taken together, the disposition of those groups — from lukewarm to outright hostile — presents a stiff challenge to Speaker Nancy Pelosi (D-Calif.) and her team as they try to forge ahead with the campaign finance measure.

“The changes will ultimately get this through to the finish line, but we’re not there yet,” one senior Democratic aide said. “We have to cross a couple more T’s and dot some more I’s before anybody is going to pop champagne corks.”

The bill, officially the DISCLOSE Act, comes in response to the high court’s 5-4 ruling in Citizens United v. Federal Election Commission in January that struck down many restrictions on political communications and the groups that fund them. The proposal would bulk up disclosure, political coordination and disclaimer requirements, and impose new limits on political involvement by government contractors and foreign governments.

A key question for leaders is whether the objections from the Chamber of Commerce, the Right to Life Committee and other largely Republican-friendly groups will spook a sufficient number of centrist Democrats to keep the measure from moving forward.

A chamber representative said the business lobby is intensifying grass-roots and lobbying efforts to sink the package — including making the point to Democratic fence-sitters that the vote will factor into the group’s decision-making about how it deploys campaign resources.

And the Right to Life Committee, an anti-abortion-rights nonprofit group, on Monday sent an action alert to its members asking them to register their objections with their lawmakers. Douglas Johnson, the NRLC’s legislative director, said the group’s opposition to the bill has now taken precedence over its opposition to Supreme Court nominee Elena Kagan.

The American Society of Association Executives — the trade group representing trade groups — jumped into the fray Monday as well. ASAE President John Graham wrote to House Members outlining four pieces of the bill “that could impede upon the First Amendment rights of private associations.

Important forces on the left remain wary as well. Bill Samuel, the AFL-CIO’s top lobbyist, said the labor union “still has a few outstanding issues” relating to the effect of the bill on its local unions and labor councils. “The effect is pretty far-reaching, and I’m not sure it was intended to be far-reaching,” Samuel said.

“We support the thrust of the bill, the goals of the bill, and we hope to be able to support it,” he said, adding the labor giant has “made progress” in talks with House Democratic leaders.

The Sierra Club likewise endorses the concept of the bill insofar as it is aimed at increasing transparency in campaign financing. But Cathy Duvall, the group’s national political director, said the bill still falls short in distinguishing between political activities that should be subject to greater public scrutiny and legitimate lobbying activities that the bill would restrict. “It would significantly impact our ability to do legitimate legislative grass-roots lobbying, and we’re still having conversations to see if we can support the bill,” she said.

Duvall called the carve-out that leaders engineered for the NRA “undemocratic.” And Nan Aron, president of the left-leaning Alliance for Justice, blasted it. “We can’t have two tiers of free speech in this country, with one set of rules for the big guys and another for everyone else,” Aron said in a statement. “This outrageous attempt to garner support for the bill does nothing more than make the already powerful even more powerful and undermines both the stated purpose of the legislation and fundamental Constitutional principles.”

Under the deal, the NRA would be exempt from the disclosure requirements that the group’s officials complained would force them to make their membership lists public. The text of the amendment making the change never mentions the NRA specifically. Instead, it grants an exception to any 501(c)(4) group that claims more than 1 million dues-paying members, with a presence in all U.S. states, that has existed for at least 10 years, and derives no more than 15 percent of its funding from corporate or union sources.

It is not clear which, if any, organizations besides the NRA meet those standards. The Sierra Club, for example, claims about 750,000 dues-paying members. And the NRLC is a federation of 50 state-level groups, each of which is incorporated separately, and none of which has membership approaching 1 million.

In crafting the compromise, Democratic leadership, led by Rep. Chris Van Hollen (Md.), the architect of the bill, tried to steer a middle course between accommodating the NRA, which could single-handedly tank the package, and government-reform groups that wanted the narrowest exemption possible.

“Reforming the system is something that Washington tends to resist, and we did the best we could here,” one Democratic aide said. “It’s about as far as it can go in terms of changes that address a significant number of folks, maintain the support of the reform community and have some teeth.”

An NRA spokesman declined to comment, pending the public posting of the amendment package that includes its fix. But Democracy 21 President Fred Wertheimer blessed the deal. “This exemption has been deemed necessary to pass the bill, but since it is so narrow it will not open a major loophole in the legislation,” he said in a statement.

At least one group was considerably less supportive.

“This proposal is so outside the spirit of what Congress says it is trying to do that any supporter of real reform should be embarrassed to vote for it,” Paul Helmke, president of the Brady Campaign to Prevent Gun Violence, said in a statement.

Democratic leadership sources said the measure could hit the floor as soon as this week. That will depend on whether leaders believe they have the votes to pass it.