Although the Senate in April blocked a bipartisan proposal to expand background checks, Senate Majority Leader Harry ReidHarry Mason ReidFive takeaways from testy Heller-Rosen debate in Nevada Major overhauls needed to ensure a violent revolution remains fictional Senate heads home to campaign after deal on Trump nominees MORE (D-Nev.) has vowed to reconsider the bill before the end of the year. Meanwhile, advocates are using the Newtown anniversary as a platform to redouble their pressure on Congress to revisit the issue.

As a part of that effort, New York City Mayor Michael Bloomberg (I) this week asked wealthy donors to withhold funds from the Senate Democrats who opposed the background check bill in April. And the families of Newtown victims met with Speaker John BoehnerJohn Andrew BoehnerHouston Chronicle endorses Beto O'Rourke in Texas Senate race The Hill's 12:30 Report — Presented by Citi — House postpones Rosenstein meeting | Trump hits Dems over Medicare for all | Hurricane Michael nears landfall Kavanaugh becomes new flashpoint in midterms defined by anger MORE (R-Ohio) and Minority Leader Eric CantorEric Ivan CantorTrump gives Dave Brat his 'total endorsement' Former TV journalist gives GOP rare dose of hope in Florida Dave Brat trailing in reelection bid MORE (R-Va.) Wednesday to urge tougher laws.

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Hoyer said BoehnerJohn Andrew BoehnerHouston Chronicle endorses Beto O'Rourke in Texas Senate race The Hill's 12:30 Report — Presented by Citi — House postpones Rosenstein meeting | Trump hits Dems over Medicare for all | Hurricane Michael nears landfall Kavanaugh becomes new flashpoint in midterms defined by anger MORE agreed to the meeting because “he is an empathetic person” who wants to show respect for people who have suffered great loss.

“But I don't know that they will move him to action,” Hoyer added.

Behind Boehner, GOP leaders have said for months that they would wait for the Senate to act before considering new gun laws in the lower chamber. But Rep. Bob GoodlatteRobert (Bob) William GoodlatteConservatives fume over format of upcoming Rosenstein interview Rosenstein to appear for House interview next week Fusion GPS co-founder pleads the Fifth following House GOP subpoena MORE (R-Va.), chairman of the Judiciary panel, which has jurisdiction over gun laws, told The Hill last month that he's had “a lot of discussions” with Boehner on the topic, suggesting the House might tackle the issue independent from the Senate.

“We are trying to improve the system to keep people who are barred under the law from owning firearms from getting access to them,” Goodlatte said. “We don't think the things that were proposed in the Senate do that. So we have not backed away from trying to figure out how to improve that, but we've made no decisions yet about what to do.”

Advocates are hoping that public opinion polls — which show support for expanded background checks — will force opposition lawmakers to rethink their position. Two new surveys released Wednesday by Bloomberg's group, Mayors Against Illegal Guns, found that voter discontent with Sens. Jeff FlakeJeffrey (Jeff) Lane FlakeCongress raises pressure on Saudi Arabia Flake says he and his family got death threats 'from the right' Trump boosts McSally, bashes Sinema in Arizona MORE (R-Ariz.) and Kelly AyotteKelly Ann AyotteElection Countdown: O'Rourke brings in massive M haul | Deal on judges lets senators return to the trail | Hurricane puts Florida candidates in the spotlight | Adelson spending big to save GOP in midterms GOP mulls having outside counsel question Kavanaugh, Ford Pallbearers, speakers announced for McCain's DC memorial service and Capitol ceremony MORE (R-N.H.) continues to grow two months after they opposed the background check bill.

“Both senators have suffered for their votes against legislation that is overwhelmingly supported by Arizona and New Hampshire voters,” the survey results claim.

To pass the background check bill, Reid would need the support of five additional senators to defeat a likely GOP filibuster.

Hoyer, for his part, is pessimistic the House would act even if Reid is successful.

“I would hope that they would move it here, but I don't see any indication that the Republican leadership — even Mr. Boehner or Mr. Cantor or Mr. Goodlatte — has any intention of doing something,” Hoyer said. “We will see.”