House Democrats are pushing forward today with a measure to strike back at the controversial Supreme Court decision loosening restrictions on political spending. But leaders are split on the strategy for advancing the bill — a debate that highlights broader Caucus tensions over how best to prepare the party for potentially brutal midterms.

Democratic top brass agree on the urgent need for a legal bulwark against what could be an unchecked flood of spending by outside groups this election season after a divided high court ruled in Citizens United v. Federal Election Commission, striking down many restrictions on televised political advertising.

But while Speaker Nancy Pelosi (D-Calif.) and most of her lieutenants want to pass the measure before the Memorial Day recess, Majority Leader Steny Hoyer is urging caution. The Maryland Democrat’s camp is on edge that without some targeted fixes, the U.S. Chamber of Commerce and the National Rifle Association, in particular, will oppose the measure and exact political revenge on moderate Democrats who supported it.

What’s more, Hoyer has argued privately that there is no clear path forward for the bill in the Senate, raising the specter of forcing vulnerable Members to take a tough vote only to see the measure stall in the other chamber. That view gained credence in a Tuesday huddle of House and Senate Democratic leaders when Senate Majority Leader Harry Reid (Nev.) said he doesn’t believe the bill has the 60 Senate votes needed to overcome a filibuster.

But Pelosi and Rep. Chris Van Hollen (D-Md.) — the architect of the package and a member of leadership as both Assistant to the Speaker and chairman of the Democratic Congressional Campaign Committee — believe House passage will goose the Senate version.

The struggle over how to proceed reflects a larger challenge for House leadership as the team steers through the remaining items on the agenda with an eye toward November. Democratic-allied interest groups are pushing the majority to keep taking gut-check votes — on gay rights measures, immigration reform and others — in the hopes of breaking through while the party still has comfortable margins in both chambers. Battle-weary vulnerable lawmakers, however, are looking to duck incendiary debates so they can focus on defending the records they’ve already compiled.

The do-it-now camp argues that whatever tweaks the campaign finance bill needs can be made as it advances. To that end, after some uncertainty earlier this week about scheduling, the House Administration Committee today is set to mark up the measure, setting up possible floor consideration next week. And to the charge that swift action could prove bad politics for marginal Democrats, those trying to speed its passage point to deep public disapproval of the Supreme Court ruling. A Quinnipiac University poll in late April found 79 percent of voters oppose the decision. And a Washington Post-ABC poll in late January found 72 percent of voters favor legislation reinstating the spending limits stripped by the decision.

But it’s not the general population that some moderate Democrats are nervous about — instead, it’s powerful political groups that could mobilize to defeat vulnerable lawmakers who help put the measure over the top. Democratic leaders have stepped up their outreach to outside groups across the ideological spectrum in recent days to explain the measure and give assurances against unintended consequences. Pelosi on Tuesday huddled with AFL-CIO President Richard Trumka, for example, and a spokesman for the group on Wednesday said talks were ongoing.

“We’re hopeful the final legislation will address our concerns,” the spokesman said. And Hilary Shelton, director of the NAACP’s Washington, D.C., bureau, said that after speaking with Majority Whip James Clyburn (D-S.C.) and Van Hollen, he is confident “they are now working to make sure our concerns are addressed.”

But the twin bogeymen for leaders remain the U.S. Chamber and the NRA.

The precise nature of the groups’ concerns are not clear — neither would comment for this story. Of the two, Democratic leaders are more nervous about the gun lobby, thanks to its proven ability to sink measures that it opposes by flipping dozens of pro-gun-rights Democrats. The NRA’s concern appears to center on the possibility that under the bill, its political expenditures could force it to disclose individual membership, according to people familiar with the group’s thinking. The organization seems to have stepped up its activity on the matter in recent weeks, hiring Vickie Walling — former chief of staff to Rep. John Tanner (D-Tenn.) and a key staffer for the Blue Dog Coalition — in part to lobby on “campaign finance reform legislation,” according to a lobbying disclosure.

The bill so far includes several moderate co-sponsors that champion gun rights. Rep. John Boccieri (D-Ohio), a vulnerable freshman who has co-sponsored the measure, said the Supreme Court ruling “handed over the keys to electoral government to big corporations and unions.” He said he was unaware of any opposition from the NRA. Asked what he would do if the NRA came out in opposition, he said, “There’s a lot of if’s and could be’s. If they do, we’ll cross that bridge.”

Speaking privately, other moderates raised serious doubts about the advisability of moving forward. “It’s like poking a bear,” one chief of staff to a vulnerable lawmaker said. “If the Senate doesn’t do it first, there’s very little chance it’s going to happen, and then, what’s the point?”

Sen. Charles Schumer (D-N.Y.), who is sponsoring the companion measure, has struggled to find Republican co-sponsors in his chamber, even as Van Hollen coaxed two House Republicans — Reps. Mike Castle (Del.) and Walter Jones Jr. (N.C.) to add their names to the House version. The New York Democrat said the plan “has been for the House to go first, but I don’t think we need to. I don’t know. … They usually go first.”

Either way, the bill has strong backing from the White House. President Barack Obama caused a stir in his State of the Union address when he called out the Supreme Court justices seated before him for the decision — a rare interbranch slight. And he has spoken frequently since of the need for a legislative fix addressing the decision. “The president strongly supports this bipartisan bill, which would establish the toughest-ever disclosure requirements for election-related spending by special interests,” a White House official said, adding that Obama “looks forward to signing this critical legislation in the near future.”